ADU on Duplex R2 lot question

[Tess Sweet]

We are in escrow on a duplex zoned R2 that has a detached garage that was converted into an additional unit without permits. The housing department states that it needs a new certificate of occupancy because it's no longer a garage. How can we go about making this a legal unit? The lot is big enough for 3 units because its 7700 square feet - but its zoned r2. Anyone know how hard it is to attain zoning variance? We don't want to have to tear out what has been built in the garage. (They did nice work! And we wanted to live in it while we fix up the duplex...)