Buy a new antenna and booster unit for your radio. The quality of the signal you receive is hugely influenced by the standard of your equipment. If you have an old or inferior antenna, it's likely that this will be at least partly responsible for the instability you're experiencing. You can pick up a new antenna and booster unit from most electrical or AV stores and online.
Move your antenna around the house to establish where you receive the best signal. If you have an external antenna on the roof of your house, try moving this into another position to optimize your signal. You may need to move the radio to get the best signal possible. If your antenna is inside, position it close to a window and away from walls made of concrete or steel.
Tune your FM receiver to the strongest signal available for the station to which you're listening. Some stations will broadcast on a range of frequencies that will be grouped closely together on the FM dial.
Move your radio receiver away from other electrical equipment that might be causing interference. Computers, TVs, microwave ovens and cell phones can all interfere with your FM receiver's reception. If you can't move your radio or the units that might be causing interference, make sure they're turned off when you're listening to the radio.
Try another station. You might not live in the right area to pick up the station you want to hear. If you live outside of the broadcast area of a station or beside a hill or in a valley, chances are that you won't get a good signal without some expensive equipment.