Ask at a good pet store about wet wipes for cats. These are designed to keep the dander down that cats give off, which is what causes allergies in people.

A friend of mine had her grown daughter living with her for a while, and the daughter had two cats. My friend is very allergic - they tried the wipes and the result was fantastic!

ETA: My cousin has always loved cats, but her allergy sent her to the hospital when she was a little girl. When she got married later on, her husband had one cat. She decided to stick it out and over time - several years - her allergies diminished!