Unless she is allergic to latex, what would be her argument? . . . It literally would feel the same to her.
Are you sure she is not trying to get pregnant?
Girlfriend won't do it with a condom, how do I convince her that we need to use one?
Get another girlfriend!
Morality aside, are you concerned about STD's or just wanting to use an additional form of birth control---assuming she is in fact using one?
I assure you that condoms break, Stud.
Simple. You don't have sex without one. Since there are a variety of condoms out there, you have the option to experiment and see which one will work best.