1997 Subaru Liberty RX which keeps overheating. Have been told that it is the heater core but that it will cost $560. Does this sound about right and is there any alternative to replace it?

sounds kind of high ask someone else and sometimes you can bypass the water hoses but them you lose the heater and you could call a parts store and ask what the price is for a heater core they are hard to replace most of the time on all is why its high sometimes takes a couple days to replace them

It is possible, some cores r labour intensive to replace. Call a couple more shops to verify, & if u get a really low quote, look in a shop manual. l had to replace a heater fan in a car some years back. l got labour estimates from $50 to $300. l went by the manual & did it mayself. l discovered the $300 estimate was probably correct, as l had to take apart a lot more than l expected. Everything l took apart was the same l would have done to get at the heater core.

If the car is overheating it is probably the headgaskets. Many Libertys (Legacy) came with the DOHC EJ25 engine, notorious for overheating.

The heater core has nothing to do with the vehicle overheating unless it is leaking and you would know this because the carpet inside would be soaked.
To replace the heater core you need to take out the complete dash. Like one other person said, you could bypass it, but you will have no heat.

Does your car lose coolant, overheat while sitiing still or while moving?