Your god will not give you random prayer boons until after you have received a sacrifice gift from them. (They will still fix troubles when you pray.)

Gifts from your god (including gifts not from sacrifice, such as spellbooks) should have their blessedness identified, since your god is very explicitly blessing them.

Wielding Mjollnir (or potentially any artifact) after it was gifted by your god requires the god to spend constant divine attention on powering it. In game terms, this means that your prayer timeout will never drop below some minimum of a few hundred turns, because the god will not take kindly to requests for more assistance after they are already constantly giving you it.

Track whether or not you have ever worn an armor piece in each slot. When you receive a non-artifact sacrifice gift, slightly bias towards slots for which you have never worn armor.

Your god may give you useful non-artifact items as sacrifice gifts, such as a stethoscope or bag of holding, so long as you aren’t carrying one of them already.

A slightly more advanced system that wouldn’t require carrying a bunch of items to avoid getting duplicates would be to track the last time you picked up or put down each type of object, and if you have never touched one or it’s been a sufficiently long time, you are eligible to get that item as a gift.

In variants where your god can gift non-artifacts, they should sometimes gift you a stack of projectiles (ideally they can match it to some ranged weapon you have if they are feeling nice). It would be useful even when the player already has a favored melee weapon.

Several elaborations on a system for more reliable (and less tedious) gifts from altars:

1. Your god will always give you a gift on the first sacrifice from a given coaligned altar (not if attempting to convert an altar). But after that, they will not give you any more gifts on that altar no matter how much you sacrifice. (Other sacrifice effects will still happen as if you failed the die roll for a gift.) This eliminates all the tedium associated with altar camping for gifts (though not all altar camping in general), but is a significant change since getting one corpse to an altar is much easier than getting multiple ones, and streamlining the game to this extent may be undesirable.
2. As above, but the gift will only be given for the first monster whose difficulty is above a certain threshold (possibly partially dependent on depth, and also with some random factor). Thus, if you sacrifice and get no artifact, you know you have to try a harder monster.
3. The total difficulty of monsters sacrificed is accumulated; the first sacrifice to put you over some threshold (say, 30 cumulative difficulty) is guaranteed to give you a gift. The totaling may or may not be per-altar.
4. Your god has a set list of rewards, each of which is tied to some monster difficulty level. Some of these rewards are artifact gifts; others may be things like luck. You only get a gift when you sacrifice a monster of the requisite difficulty, and thereafter monsters of equal or lesser difficulty to that are ignored by the god for reward purposes (they may still be used for mollifying and decreasing prayer timeout). If you make a sacrifice that earns you multiple rewards at once, you either get them all at once or you get the biggest reward and the smaller ones on subsequent sacrifices. This would enable game developers to fix a number of artifact gifts (say, 3), by encoding that many rewards for them. This system might have problems in games with no deep usable altars where it is harder to get randomly generated difficult monsters.
5. Variation of the above: at the beginning of the game, three random monster difficulties are chosen (with some limiting on ranges). Sacrificing a monster of a difficulty above any of these thresholds automatically gives you a sacrifice gift and removes the highest remaining threshold you met.

In variants where your god can gift non-artifact items: Track which items have been gifted, and never gift “duplicates” - e.g. don’t gift a suit of armor if one has already been gifted in the current game, or a second battle-axe.

After gifting you an item, your god doesn’t give you anything else until you’ve used it to their satisfaction. Such as killing a certain amount of monsters with it if it’s a weapon, wearing armor for a certain number of combat turns, and so forth.

This sacrifices gameplay fun for improved flavor and balance, so tread carefully if implementing it.

You can get at most 1 sacrifice gift from any given altar. It can still be used for sacrifices and everything else, but you will never again get a gift from it.

Chaotic gods in FIQHack should sometimes grant potions of wonder as a sacrifice gift.

Giftless conduct, which is broken when receiving divine gifts from sacrificing. Possibly also when receiving an artifact via crowning.

Artifacts have a minimum XL associated with them. You can’t get a given artifact through sacrifice until you are at least its defined minimum XL.

Sometimes when your god is angry at you, they will grant a gift when you sacrifice to them. But the gift is a negative item, because the god is trying to kill or mess with you.

You occasionally receive a dragon egg as a sacrifice gift.

Convicts can uniquely get their god to unpunish them as a special prayer boon (or maybe sacrifice gift that replaces an artifact). This requires some prerequisite like a certain amount of alignment record, so that it can’t randomly happen only a few hundred turns into the game.

Define a “power level” or a “tier” for each artifact, and when gifting an artifact, use the player’s experience level and other stats to calculate an appropriate tier to gift an artifact from. The only reason it feels bad to get Giantslayer is because you know you could have gotten something much more powerful but randomly didn’t; if the more powerful artifacts were simply not possible to get due to you not having the right stats yet, this might not happen as much.

Remove the feature where being gifted an artifact in a restricted skill unrestricts it to Basic; compensate for this by fixing the balance of artifact base types and the gifting logic so that your god’s first gift to you is never an artifact whose skill you’re restricted in.

If you are wielding a non-artifact weapon, and happen to get gifted an artifact whose base type matches your weapon, your weapon will be converted into the artifact (keeping its existing enchantment).

Only knights of XL 7 or higher can dip for Excalibur; but Excalibur is available as a lawful sacrifice gift.

Gods can grant you (unique?) pets as a sacrifice gift, or possibly a prayer boon. Example here was Sleipnir for valkyries. If it’s a steed, it will always be saddled.

If a god doesn’t have any good artifacts or spellbooks to grant you as a sacrifice gift, they give you a prayer boon instead.

Add one or two artifacts or modify artifact base types such that there is more than one good blunt artifact you can obtain through sacrifice. (The current three are Mjollnir, which is decent, and Ogresmasher and Trollsbane, which are not.)

At the start of the game, three artifacts are selected as potential divine gifts, and you will never get any other artifact than these three by regular sacrificing. These three artifacts must not hate the player’s race and ideally will provide a good balance in terms of power and utility. Gods can also grant non-artifacts as gifts, which no longer count against your odds of receiving an artifact. Also, the chance of getting an artifact is biased against low-level characters who have not made many sacrifices and towards high-level characters who have.

When a Priest is gifted an artifact weapon, they are unrestricted in its skill and their skill cap in it is set to Skilled, rather than Basic.

God gifts come pre-identified: artifacts automatically become known (so that you get “the Giantslayer” rather than “a long sword named Giantslayer”; non-artifacts automatically become type-identified. At the same time, it may be useful to newer players to not hide the artifact’s base type, so perhaps the artifact should not become learned (though identifying its enchantment, etc is still fine).

Multi-skill gifted weapons should unrestrict all of their skills.

Monks will only get gifted weapons whose skill they have previously trained at some point.

As part of artifact rebalance: guaranteed sacrifice gifts should probably not be ascension kit quality gear, since otherwise sacrificing for such gear becomes a dominant strategy. (Most important for weapons; you don’t want to be able to obtain a weapon early that will obsolete all other weapons in the game.)

Gods may grant a saddle as a sacrifice gift and unrestrict riding skill.

Other priest benefits: the chance of receiving a sacrifice gift is doubled, make it easier to get crowned or other high boons, the prayer timeout isn’t increased when crowned.

When a god decides to give you a gift and you are already wielding a weapon of the same type, the wielded weapon becomes the gift, and retains its original enchantment and beatitude. Erosionproofing is still added if the weapon doesn’t have it.

Every hit with a wielded weapon, up to 20, decreases the chance of being given a non-weapon artifact.

Gods are more likely to give gifts for higher-difficulty sacrifices.

Your god respects any conducts you currently have when giving you stuff. If illiterate, will not give you a spellbook. If weaponless, will not give you artifact weapons (maybe could give a +1 intrinsic damage bonus instead). If pacifist, may send tame minions. However, this is only if your deity is lawful or neutral - chaotic gods will ignore these rules and give you whatever.