NotYoda FIV isn't a big deal at all generally. Most cats with it seem totally unaffected and end up dying of old age. We also don't say that FIV cats need to be kept indoors. Gracie needs restricted access to the outside because of her paw, not because of the FIV.
As a general question though about having a garden but not letting a cat out, well that would be fine if you get a cat that isn't bothered about going out, but it would be very difficult if the cat actually wanted to go out but shouldn't for some reason as you will probably find it difficult to physically stop the cat from going into the garden and would also probably make you feel guilty.
I think a middle aged/old cat would be your best bet. They tend to like to sit in the sun but aren't bothered about or aren't physically up to chasing birds.
We do have lots of cats though so it's normally possible to find the right cat for the right situation and there isn't much that we rule out totally provided that the potential owners are sensible and that they are willing to consider a cat that would suit their situation.
For example we recently turned down a home that was right next to a busy road with only a very low wall between the garden and the road. We said we would be happy to give them an older, street-wise cat, but they insisted on young cats/kittens. When we said they would probably end up dead they said 'well that's just a risk you have to take isn't it?' No, it damn well isn't!