Both pet rabbits and wild rabbits can indeed carry some disease if they're infected with the diseases however it's very unlikely to get diseases from a pet rabbit that is never in the wild around other rabbits.
For the pet rabbits to get diseases they would have to come into contact with other rabbits or animals that have those diseases so if they do not come into contact with the other animals or rabbits with the diseases then they could get it.
But as long as the rabbits are not coming into contact with other wild rabbits or animals then they should not get the diseases.
If the rabbits do get diseases then they can carry the diseases such as the hantavirus, leptospirosis, lymphocytic choriomeningitis (LCMV), Tularemia and Salmonella.
But once again it's very unlikely that the pet rabbits would give you any diseases.