Do NOT offer to let him keep the car and make payments on YOUR loan.
His choices are:
1) Get his own loan and buy the car from you
2) Give the car back to you, you sell it and close out the loan... and he goes and gets his own car.
That's it. Expecting an alcoholic to make good on payments on a loan in YOUR name is a recipe for disaster.
P.S. I say this because I JUST went through this with my AH... except it was ME that has use of the car. I tried to get a loan to refinance the joint one under my own name (buy AH out)... miles/age were too high to refinance... so I traded it in and bought a car just for me, with only MY name on it. It's simple, clean, and permanently cuts the financial tie.