and cost more to rekey, you might want to consider one-time investment for installing "Smart Key" lockset. These are not very expensive, you can get for $120 at HD or Lowe's.
Once these are installed, you can rekey by yourself (takes seconds) any time you want.
However, in your case, I honestly think you should let the tenants know that they will need to pay for the rekey if they insist on having it rekeyed. (This should already in lease terms - I always put this in lease). You should explain to them that the locks are recently rekeyed/installed and no one except ... have touched the key.
