Hello,
to my opinion, decoding of an ideal FM signal shouldn't be a problem at all. It can be reduced to simple frequency respectively period intervall measurement, as suggested in the previous post. In this case, i see no particular purpose of using a sine rather than a squarewave signal at the transmitter.
I guess, the a sinewave carrier is used, cause the FM signal shall be transmitted by a channel. But how does the signal look at the receiver? Decoding of a noisy signal actually could be an issue, with low SNR (signal-to-noise ratio) even impossible with simple period measurement.
That's the point where digital receiver techniques come into play. There are many options, a general technique is using a digital PLL to track the carrier. With the intended f/2f FSK modulation, a special PLL construction could be used, that locks to both f and 2f (assuming the carrier phase is continous and not changing arbitrary).
Regards,
Frank