Has your bf considered allergy shots? They would probably work for him. If he didn't immediately react to the cat violently, chances are he isn't super allergic. I should know as I have SEVERE pet allergies and react immediately with hives/wheezing/etc. when I'm around animals.
The allergy shots have done wonders for me and I don't have to be on meds everyday. I have my cat, Suki, who I refused to get rid of when I found her as a stray. I will say from experience that the allergy shots and just being around her constantly have reduced my reactions to her almost completely. I do occasionally have an outbreak around her, but those are few and far between now.
I would look into your options before giving up your baby!