You can use the portal array of services for drivers:
Unfortunately, you can do only a few procedures online for now, but you can definitely save some time by pre-filling the form, paying the receipts, book the time for the visit.
At the moment, the service is not yet available in whole Ukraine (only works in Lviv), but, according to Dubilet, it will launch in other areas soon.
You can join the volunteer developers group of iGov here (UA).
We also recommend you read: IGov portal will help to register business in a few clicks.