Many people just spell the word "gym."
The general sign for GYM looks like a cross
between lifting weights an jumping rope. The position of the hands
are up near the shoulders.
That handshape is a modified "X." The thumb is pressed up
against the bent index finger as if holding a rope.
At the college where I teach (my day job) we regularly have
department meetings. Before and after such meetings (and sometimes
during, heh) I like to ask the various interpreters how they sign
whatever concept is on my mind that day. Freelance terps are great
sources of current and emerging sign variations because such terps
regularly interact with a wide variety of Deaf people in a wide
variety of settings. When asked "How do you sign G-Y-M?" - most
terps (and native Deaf adults) respond with some variation that
looks like a cross between jump rope and "lift weights." The
handshapes vary a bit, but generally the handshape looks like you
are holding a jump-rope in your hands. Some people do this
sign with "G" handshapes but I don't recommend that.