A twin mattress is 75” long, so all daybeds are going to be at least that size. You’d have to do more of a chaise or pullout sofa. If you get something custom built, and use a memory foam twin mattress, it’ll probably fit snug in the space, but double check first!

A memory foam or gel foam twin mattress can be cut to size with an electric knife.

There are baby cribs that convert to daybeds. They're about 53" long.

I need to see wehre it is going. Why a daybed if there is space for a sofa bed? You could just have a custom base made and order a memory foam to fit.