I agree that BC547 isn't the best choice but it shouldn't casue the frequency shift you are seeing.
Yes, you can make a new capacitor value by connecting two (or more) in parallel or in series. In parallel just add the values together, in series it's a little more complicated, the formula is 1/C = 1/Cx + 1/Cy where x and y are the two individual values so you have to add their reciprocals then take the reciprocal of the result. For 1 - 2 pF you can make your own capacitor from about 1cm each of thinly insulated wires twisted tightly together, except for the ends you solder to the board of course!
You said the frequency was stuck at 60MHz regardless of the tuning capacitor position. My point was that it the tuning capacitor was faulty it could only be that it was open circuit (connection to the capacitor plates was disconnected). If it was short circuited the oscillator would not run at all. However, an open circuit tuning capacitor would make the frequency go higher, not lower. Adding capacitance across the antenna connection to ground would have the opposite effect and make the frequency lower, if you had been connecting an antenna through a screened cable it might have accounted for the lower frequency. The way the antenna affects the frequency is why these simple circuits are frowned upon by many of us. They tend to drift in frequency and change tuning as you move objects close to the antenna. What might seem to be working perfectly one minute could shift tuning and interfere with another signal in the next.
Brian.