Try Nikolai Minev, who lives in Sheremetya (short way up the road next to the Serbian Grill). He has limited English, so I would recommend you text him in the first instance. He will probably want to be picked up and returned home. He has a "day job" so does the tuning mostly at weekends. Expect to pay 20-50 levs depending on how "out" your piano is.
Will PM his number.