When it’s about FM transmitters most of the people think about complicated circuits with LC oscillators, tuning problems, pcb coupling issues and the high risk of failure. You can find dozen or more schematics on the web, I personally tried a few, but without luck because I couldn’t tune in the oscillator.
The mathematical background is complicated, but well explained for those interested, the code is written is assembler which is a must since the tight timing. Beside the inductor all of the components are widely available, this must be hand made and by stretching you can fine tune the oscillator, thing which will be probably needed.
By using surface mount components the pcb size could be greatly reduced, but keep in mind when making the layout to reduce coupling and noise susceptibility.
Make sure that you don’t disturb any local frequencies, or somebodies privacy with it.