You do not have to deny a service dog when there are at least a half dozen other reasons to deny any applicant. Here they go. Tell your tenant one or more of the following:
1. Credit score is below 700. A failing credit score is whatever you want it to be. 2. Not enough time at current job. 3. Lack of verifiable rental experience with someone other than friends or relatives. 4. No landlord references from last three places of residences from other than friends or relatives. 5. One or both applicants have a criminal record. No crime is minor. 6. More than two occupants per bedroom. 7. Income is less than 3X's rent. Do not include child support.
Jake, those are interesting reasons for denying an applicant, however, if these are not the same criteria you use for applicants w/o service animals then you lose. Apply the same criteria to everyone (remember a service animal is not a pet so none of your pet related criteria apply) and you will survive as a landlord.