How do I add applesauce to a cake recipe?

I'd probably start by replacing the beer with applesauce -- depending on how wet the batter is it could work as a 1:1 replacement, but you may need to add extra liquid if it's too dry. You can replace melted butter with applesauce as well, but I think you'll have less textural change by replacing the beer. If you go with the fat replacement, start by only substituting half (or less) with the applesauce.

Applesauce can be substituted for OIL in a recipe, not for eggs, molasses, buter, or beer