When your property was built, your city likely dictated a certain number of handicapped spaces. Those have nothing to do with your renter's request. She is asking for a 'reserved space' and it should not be the blue handicapped sign. Use a different color, no wheelchair symbol, add a permit number. (not apartment number or name) Using a standard handicapped sign allows anyone with a handicap/disability permit to park there. If she indeed has a disability, you are required to provide a reserved space.
Check with your city, state, housing authority...sadly the advice you get from well meaning people can get you sued.
We feel for the smaller properties, especially for seniors, who have very limited parking. Yes, you could end up with all reserved parking. Yes, if you CANNOT see the disability, if it isn't obvious, you can request a health care provider's document. Do not ask the nature of the disability, just verify that she has one.