Replacing rear derailleur
 

Take a look at Microshift 9-speed mountain derailleurs. Inexpensive and good quality, and can be found from many sources on eBay. They are compatible with Shimano pull ratios for indexing.

Is that a 'rapid rise' model?

I have #760 one that you can have- I hate that dyslexic POS.

Any 9 speed mtn bike RD should work fine- long or med cage to match what you have.

I like this one: https://www.amazon.com/MicroShift-Ma.../dp/B00FSRUOUQ

You can replace it with a new Shimano 9 speed MTB derailleur. Shimano changed the cable pull when they went designed the 10 speed MTB derailleurs (labeled as Dyna-Sys) so only a 9 speed (or earlier) will work with the shifters you are probably using (I assume indexed) . You can use either the

Shimano RD-M771 XT 9 speed Rear Derailleur - which has what I think of as a classic look

OR

Shimano RD-M772 XT 9 Speed Rear Derailleur - which has the "Shadow" lower profile body with direct cable routing

They are about $60 to $70 new. Both have the traditional "top normal" return spring (i.e., the derailleur moves to a smaller cog when you loosen the cable tension). Make sure you get the correct length (GS medium cage or SGS long cage). If in doubt go with SGS.

Even a 9 speed Acera or Alivio RDER will do the job fine.