I had a molar pregnancy 5 months ago and my levels have stayed down since and I have been on birth control (implant) and I'm about to get it taken out because of certain side effects . My doctor wants to put me on a different contraceptive right after , but I don't want to be because none of the various types of birth controls have really been good with me . How long do I have to wait until a possible slip up of unprotected sex is all right ?

I'm confused. Your title suggests you want to try to conceive yet the context of your post suggests you want to know how long your implant might work after its removed? Hmmm... I'll try to answer both

After molar pregnancy, its advised to wait 12 - 18 months before trying to conceive again.

After your birth control is removed, you could become pregnant immediately if you don't use protection. If you don't want to get pregnant you cannot have a "possible slip of unprotected sex"