100 periods is about what you will get with a high quality (low loss) capacitor, like a pulse rated polypropylene capacitor and a well designed layout. Dumping a capacitor into the coil using a spark gap will give you an exponentially decaying waveform, where the amplitude will be roughly 1/e (37%) times the initial value after Q cycles, where Q is the quality factor of your resonant circuit, or the ratio of energy lost per cycle to the total stored energy. If the capacitor and the wiring is done well, the Q factor will mainly be limited by the coil itself, and it will typically be a few hundred in this frequency range.
The physical size of the coil gives the inductance, as you can not practically have more than one turn (with the required voltage, it would be hard to insulate the coil properly), in this case about 36 nanohenries. Since the frequency is given, you can calculate the needed capacitance, which will be around 180 nF to get 2 MHz. The di/dt is higher than most available thyristors can handle, and the circuit impedance is low enough that any practical MOSFET will introduce too much damping, so a triggered spark gap or the vacuum tube equivalent is the only practical way of switching it, as far as I know.
To change the frequency, you can switch parts of the capacitor bank in and out using high voltage relays. You can do binary scaling of the switched capacitor values to minimize the number of relays. If you have N relays and N banks of capacitors with values, C, C/2, C/4, C/8 and so on, you can get any capacitance from C/2^N to 2C, with a step size of C/2^N. For example with C = 1 uF and N = 8, you would get any capacitance from 4 nF to 2 uF, with a step size of 4 nF.
Note that you need to make a capacitor bank with very little parasitic inductance, otherwise most of the magnetic field will end up inside the capacitor bank itself, induction heating the capacitors and anything around them. Consider the fact that the work coil cross sectional area is a few square centimeters, the loop area of your capacitor bank ideally needs to be less than this. If you're using a bunch of cylindrical PP capacitors, consider putting each series string into reasonably tight-fitting copper pipes to minimize the loop area, and put a bunch of these copper pipes in parallel, then it might be doable.