it should work fine if you constructed exactly as it was given in the schematic,
basically these transmitters are simple LC oscillator circuits, not crystal controlled. at such high frequecies ~ 100mhz everything , including positioning of the components are critical for stable oscillations. you might be noticing that ur transmitter is drifting, ie its frequency is changing
this is unavoidable for an LC circuit, but to make it stable, i have a few tips,
1) ground the transmitter and house it in a small metal box.
2) instead of using a long flexible wire antenna, use something stiff. like some lower gauge wire
3) lastly run it off from a regulated power supply use a 7809 regulator and power the regulator i/p with around 16v. transmitters can also drift when their supply voltage falls.
one more thing, keep your hand far away from the antenna!! otherwise the freq will still drift.
your transmitter should work fine now. feel free to let me know if you still have trouble , i might be able to help.
cheers