It depends on where you live whether or not you have any legal protection in this situation. Check with your local labor board to see what applicable laws state.
If you're concerned about losing your job because you have to say no, first you might want to try over night care with a trusted friend or relative.
Hopefully, this is something you can explain to your boss. Tell him/her that you love your job and you're happy to be there and be a part of the team, but it's impossible for you to work nights due to other obligations. Ask what the two of you can work out so that the company's needs are met, you can continue to be a part of the team, and your young child isn't left alone.