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.