Answering my own question here.

1. Charlie disappears to Thailand, having eloped with Rose.
2. Alan finds a letter from Charlie giving him the house.
3. For a moment Alan tries to act sad and concerned that Charlie has married a lunatic, but then glee takes over and he jumps around (in tightie whities of course) screaming that life is finally going his way.
4. The doorbell rings. Cousin David from New York (David Spade) is at the door. He's exactly like Charlie, but has no money and no prospects. He's lost his bar in NYC, and he promises Alan he'll only stay a while, until "something turns up."

David Spade could play roughly the same character he has played on Just Shoot Me and Rules of Engagement.

The plot angle for every episode is Alan getting ready to throw him out each episode, but David either guilting or bribing him (with dating advice/help) into letting him stay.

Season finale: Alan gets hit with the property tax bill for the Malibu beach house, and realizes he can't cover it. His mother hovers hoping he'll decide to sell and move to Burbank. David comes up with a plan to rescue the house. Will it work? Find out next season.