FM modulation with crystal oscillator
Yes, there are crystal oscillator designs which can be "pulled" slightly off frequency by introduction of extra capacitance.  For crystals in the HF range, this is typically only a few kilohertz, but when multiplied up to VHF it could be on the same order as the typical deviation of narrowband FM voice as used in the amateur and land mobile services.

One possible modulator would be a voltage variable capacitance diode like a varactor.  Technically this would make a voltage controlled (or perhaps we should say voltage "influenced") crystal oscillator.

Note that frequencies and power levels where and at which you can legally transmit FM signals are limited.  

Also, you will not achieve enough deviation by this method for a wideband FM receiver, such as typically used for consumer music broadcast.