It would be useful to see a schematic of this project so that we could see exactly where the coil is supposed to go. As I mentioned before, I can't think of anywhere in an AM transmitter circuit where a 36 mH coil would be required. A loop antenna would be no more than about 200 µH.
To make a 36 mH choke, start with a 3/8" dia. x 3/8" long bobbin. You can make it out of cardboard if you can't find anything else that's suitable. Wind it with multiple layers of #32 AWG wire until the total winding diameter is about 1". It will be about 1500 turns, and will require about 260 feet of wire. Note, that this coil geometry will only be useful as a choke (not as part of a resonant circuit), and even then, not a great choke. I think that if a 36 mH coil is really required, then it's probably better to buy one.