With the exception of dishes with "onion" in their names, more often than not you can omit onion as an ingredient. My advice would be to first try leaving the onion out entirely, see how the dish is. If it is missing something, then experiment with:
- Onion powder: see how much you can get away with before your audience notices.
- Garlic: add more to compensate.
- Shallots and other onion-like vegetation: give it a try to see how that goes over.
It is going to require some experiment and trial & (lots of) error on your part, but you should be able to strike a nice balance in a few attempts.