That's pretty lame of your boyfriend to not believe you when you say he is the father. Hugs to you.
It is definitely possible for two people of mixed race to have a child who is lighter than either of them. Common even. Happens all the time. No DNA mutation needed.
Also skin tone can change pretty significantly over the first year of life - many/most newborns are born with skin noticeably lighter than what they will eventually end up with.
If you know for sure your bf is the only one you had sexual contact with in that time period then you know what you know and forget the drugstore tests. As I said I think your boyfriend is being pretty lame but if he needs to hear it from a test I'd ask your doctor about a referral for a more reliable paternity test.