You can wish for your god to be mollified, which has the same effect as doing it at an altar. Not specified if this should break atheist conduct, but it probably should, since you’re affirming there is a god that you want to placate.

The parser could look for “forgiveness” as the phrase to trigger this.

Wishing for “identification” gives you a full inventory identification.

You can wish for a shop type. The next shop that generates (of random type; specific shop types on special levels do not qualify) will be that type.

You can wish for health. This restores between 50% (or 75%) and 100% of your missing hit points and cures all status ailments.

You can wish for terrain types and dungeon features. These are already wishable in wizard mode; the justification is “If the player wants to wish for lava, why not let them have lava?” You are allowed to wish for a throne, because the chance of getting two or more wishes off it is tiny.

You can wish for friends. This duplicates the effect of casting create familiar.

You can wish for “polymorph”, which makes you polymorph. Possibly you get control over the polymorph.

You can wish for attributes, which increases whichever attribute you wish for. Maybe a d4 or d5 increase so it’s not inferior to a blessed potion of gain ability.

You can wish for intrinsics. This gives you any intrinsic that you can actually get in your normal form. Wishes for intrinsic reflection, drain resistance, and the like will be unsuccessful. Not sure about intrinsics normally only possible by eating jewelry.

You can wish for luck, which increases your Luck by d5 points.

You can wish for time. This decreases the turn count a bit, or alternatively gives you a large amount of movement points so that time effectively stops for everyone else besides you for a while (like what SpliceHack’s scroll of time does).

Wishing for “world peace” pacifies all non-unique monsters on the level, possibly subject to monster resistances.