MStechca,
The only input pin you were using was its Clock input which was connected to a switch, not the frequency-determining parts.
Your frequency-selection capacitors were connected to its outputs, which are shorted to either the positive supply for a logic high (which is decoupled to ground) or to ground for a logic low, so the capacitors didn't do anything. The counter wasn't switching the capacitors in and out!
Since your counter was at a distance from the tuning coil, the connecting wires had capacitance between them and to ground and served as an antenna.
Why don't you tune your transmitter with a reverse-biased varactor (vari-cap) diode? As I showed, you don't have to buy a special one, any reverse-biased diode or transistor junction will work. It can be connected directly to the tuning coil with a coupling capacitor with very short wires and its capacitance is changed by changing its voltage, with a resistive ladder connected to the outputs of your counter if you want. The counter and resistive ladder perform as a digital-to-analog converter. The varactor diode is reverse-biased so draws no current and its capacitance can be isolated from the resistive ladder with a high-value series resistor.
You can even modulate the varactor diode's voltage with the output of a preamp for the transmitter to have FM.