Frequency modulation on fpga

If I understand the question correctly, here's an idea to get the ball rolling.

Let's say you have an input clock which you use to increment a counter. Each time the counter reaches, say, 1000, you output the next sample of your waveform. This results in an output waveform at a constant centre frequency. Now if you use the value of your modulating input to add or subtract from the counter compare value, you will increase and decrease the interval between your output samples i.e. modulate the frequency. You could use a look up table to translate your input value to give the desired modulation range. For example by adjusting the compare value between 500 and 2000 you would get a modulation of 1 octave above and below the centre frequency.

This may not be suitable for your design but maybe it'll give you an idea.