Drawless variant

If the usually play results in a draw

Continue with two replacement moves until a draw does not exist

A replacement move is if no moves exist then remove any disc and play it as your colour

There already exists an arguably better non-draw variant. In a final game of a tournament, if it has to be decided in one game, typically one player selects colour, and the other one wins the game if it's a draw on the board. The highest ranked player in the tournament before the game chooses who gets which advantage.

Coin flipping is another way to determine a winner.

Or one could try Io.

Christian that doesn't really solve the discussed issue. How are ties resolved in Io?

There aren't any :)

Why not just use an odd-numbered board size?

I guess you'd have to find another arrangement for the starting tiles

"Why not just use an odd-numbered board size?"

In Othello that wouldn't exclude the possibility of a draw. In Io it does.

Ah, I missed the part where you can place your stone anywhere (and if Othello flips apply, do them).

Io trades compulsory capture for compulsory placement. Contrary to the first, the second is always possible.