The broken part is an adjustable inductor, not an oscillator. It most likely also has the capacitor built into its base. Unfortunately, the chances of finding this exact part is very remote. If the inductor has a manufacturer and part number stamped on it, then you have a better chance of finding the exact part. The main companies that make these are Toko and Murata. If you have their part number, then there is a better chance of finding it. On the other hand, you may be able to find the individual inductor and capacitor separately from a supplier such as DigiKey, Mouser or Farnell.