How can I attach an overflow cover in a bathtub with no access panel?
You don't need access from the back.

Usually the overflow tube is accessed from the bottom. If you can get to the trap then you can get to the overflow.

The trap and overflow tube come as an assembly and the overflow tube usually has two threaded bosses to mount your overflow drain cover and a rubber gasket that goes up against the back of the tub to seal it. You don't need to drill any holes in the tub itself. 

Look for a new tub trap assembly with the drain and overflow included to suit your bathroom trim design (polished chrome, brushed nickel, etc.).

Good luck!