Should I give my boyfriend this ultimatum for co-signing for him on a car?

I wouldn't co-sign for just anybody. I would only co-sign for a spouse or my own parent if they needed it. Don't just give your credit rating to anybody who asks. How long have you been with this guy, where do you see your relationship going. The reason I say this, is what would you do if you all broke up, you do realize that you would be held accountable for this debt. You better rethink this whole situation and really give it some thought, if you have and your certain that this is what you want to do, don't put any conditions for your signature cause what are you going to do if he agrees to your conditions and then after you sign, he reneges. Sounds as if you don't want to co-sign in the first place.