How do I get the black cap off the rear tire of the Murray lawn tractor? I don't want to break it. I need to change the tire as it keeps going flat.

Well, this is kind of tricky, depending on the age of the cap. But most of the time you will only end up with a small tear in it at worst. If it is the hard plastic cap, use a pair of channel locks and apply SLIGHT pressure with the jaws and work it back and forth, or use your hand. Or if it is the soft plastic use a pair of pliers and gently squeeze from the outside towards the center and pull gently.

If you have compressed air avail drill a tiny hole in center pressurize once off put a dab of silicone over hole next time you need it off just remove silicone

if you have compressed air avail drill a tiny hole in center pressurize once off put a dab of silicone over hole next time you need it off just remove silicone
I personally would have a problem with the "dust" cap having a hole drilled into it, even though he said to fill the hole with silicone.

I have pulled these using a claw hammer and even a flat wrecking bar.

I have always applied heat to soften the rubber which can then be removed easily by hand. (gloves of course). I use a standard heat gun but I suppose you could try a hair dryer.