I used Ebay and found a few sellers in the USA that had replacement parts for the joystick caps. Color is not the same as the original, but I don't mind this. I recommend typing in your Xbox Controller model number (see inside the battery flap for this) into the online store to see what options are available.
Just used this guide, thanks @dygross! Some useful tips for others though:
-Torx T9 was not needed. On this model Xbox controller, I used a T8 and did not have any issues as the fit was snug.
-As @ottohahn stated, it is NOT required to take off the rear plate to access the joystick caps. Once you remove the screws on the back of the controller, simply lift the front face plate off and then you can access the joystick and front buttons.
-The plastic side plates are very breakable. They are attached with plastic teeth that need to be carefully pushed in. I thought I did this then realized a small part of one broke off while removing the right-side plate. Take your time and you can totally do this!
@km4n is there any trick to removing the AKG face plate in step 4? I'm attempting this on a slightly different model, the N60nc wireless, and to me this does not seem able to come apart. Only the back cover, close to the ear, seems able to be removed.