Go to your local Ace hardware and get yourself a long shank Zerk grease fitting with 1/4 x 28 threads, which is the thread size for the nipple in Thompson Center guns. The fitting cost about a dollar. Also get six feet of 1/4"OD x .170"ID vinyl tubing which is about fifteen cents a foot.
Here's what the Zerk fitting looks like.
Then use a 5/32" drill bit to drill out the core of the Zerk. Start at the base end and drill through the plug that holds the spring in the fitting. After the plug is gone remove the spring and the ball bearing from the core of the fitting, then continue drilling all the way through. Here's what it looks like after drilling.
Then attach the vinly tubing - it fits very tight and will stay in place when flushing the barrel. It's quite easy to screw the Zerk into the nipple seat. It doesn't have to be any more than finger tight.