a method to (automatically) convert functions to be tail recursive?
The topic you're looking for is the "tail call optimization" and the corresponding "tail call elimination" transformation. To quote Odersky and Schinz, cited below,
Various techniques have been proposed over the years to eliminate general (and not only recursive) tail calls, mostly for compilers targeting C.
... put the whole program in a big function and to simulate function calls using direct jumps or switch statements inside this function.
... A popular technique is to use a trampoline. A trampoline is an outer function which repeatedly calls an inner function. Each time the inner function wishes to tail call another function, it does not call it directly but simply returns its identity (e.g. as a closure) to the trampoline, which then does the call itself. Unlimited stack growth is thus avoided, but some performance is inevitably lost, mostly because all the calls made by the trampoline are calls to statically unknown functions.
Another technique is Henry Baker’s “Cheney on the M.T.A.” With his technique, the program first has to be converted to continuation passing style (CPS), therefore turning all calls into tail calls, and can then be compiled as usual. At run-time, when the stack is about to overflow, the current continuation is built and returned (or longjmped) to the trampoline “waiting” at the bottom of the call stack.
Tail call elimination on the Java Virtual Machine, Michel Schinz Martin Odersky, 2001
Henry G. Baker, Jr. CONS should not CONS its arguments, part II: Cheney on the M. T. A. Draft Version, January 1994.