"You need to rethink your software design to fit the 8051 resources"

More fundamental than that: you need to decide whether the 8051 is suited to this application.

If it is, then you will have to structure your code accordingly;
If it isn't, then you'll have to redesign your hardware with a different processor that is suitable!

"2. use array of structures and function pointers for your menus instead of function calls."

That won't help - the functions will still need to be called, so he'll still end up with the same depth of nesting, and resultant stack problems!

"3. use the keyword const for constants so that they get stored in rom and save ram space."

That has nothing to do with his stack space problems
(anyway, const does not cause C51 to put things in CODE space - you need 'code' for that)