I recently came across a property that is currently built as a duplex, but is zoned as a single family home. The property was originally listed over a year ago and has since dropped the price substantially. I talked with a real estate agent who stated that the zoning seems to be the main issue that is keeping buyers away since it cannot be used as a duplex and substantial work would be necessary to convert it to a single family home. 

None of the properties in the area have driveways or garages, so all of the parking is street parking. I suspect that the area was zoned to prevent multifamily houses in order to reduce congestion on the street for parking. 

However, the property has a sizable backyard and a side yard. Although a couple thin trees would need to be removed, and there is a bit of a slope, I believe it should be possible to put in a driveway through the side yard into the backyard for a couple of parking spaces. I am thinking that this may be enough to get a variance to allow the multifamily use of the structure since it would not be a burden on the street parking. 

I have never attempted to get a variance on zoning before. Would anyone be able to provide some insight as to if it seems plausible that a variance could be granted in this situation? I assume that having this building being vacant for so long may push the city to make a variance, especially since the driveway would still alleviate the main concern of the zoning. If it does seem plausible, how long can it generally take to get a zoning variance, and how much would a zoning variance generally cost to obtain?