Most PLLs can be suitably used for FSK. I am not familiar with th NE564, but have in the past used the 4046 in that role.
Early types of CD4046 would have a maximum frequency of less than 2 Mhz, but newer variants (74HC, 74HCT) go far higher in frequency.
But, before we continue further, let me add that your modulator circuit requires output buffering to be useable. Any amount of loading, including a 10X scope probe, will throw the frequency totally out of whack.
A good buffer for this application is an n-channel JFet.