If you and your wife want to commit fraud that's up to you. Ultimately, the new landlord will figure it out and evict you, putting yet another blot on your record.
As for any potential landlord's right to deny housing based on a criminal record, his opinion counts, not yours.
I suggest you keep looking until you find a rental where the landlord is a bit more liberal about your background. Look at small apartment complexes, single family homes or multi-family homes where you deal directly with the owner. Be a little creative and you'll find something.

