Yes it is possible to generate the FM signal with LM566.... The LM566C can be used to generate FM signals upto 1MHz range..
U have to pass the modulation signal through pin number 5 (if am right)... I believe that all information u need would be given in the datasheet of LM566 which i have attached below....
I feel that the timing resistor and capacitor pins (pins 6 and 7) decide the center frequency which can be determined using the equation given in page2 of datasheet...
once u get the FM signal, u can probably attenuate it, remove noises (LP filter) and then transmit it....