Icing bag might work if it has a long nozzle, trick would be to fill it up from the bottom of the gun chamber expelling the air. If you use a spoon or ladle it will stick to that and if you push it into the chamber it will squeeze out the sides , it will not pour or drop or drip and is tricky to wipe, clue is in the name, its very "tacky". I did have a eureka moment though when I discovered that Dog Poo Bags make great easy to get on and off disposable gloves especially when cleaning up, even worth getting some if you have kingpins but don't have a dog.
Gosh guys I grease once a year, and have gone two years without greasing. My secret is Vesconite Bushes and Hard Chrome King Pins. Actually this idea started with a Australian Mining Engineer. There are many of us in the Pacific NW that use this system. Maybe You need to give up the "Old School" (bronze) and let technology solve your greasing problem. Look up "Vesconite" on your computer and get some information.
1. Whats wrong with greasing. Often! Gets You down under your Morgan for inspection if nothing else. 2. How am I sure Vesconite is superior. Because once every year, sometimes two years I take the front suspension apart and check for wear and other problems. How can I suggest Vesconite, if I don't regularly inspect it. So far so good after over 10 years and many miles. 3. Who cares anyway. I am 86 and I don't like crawling under My Morgan at a Motel while on a trip. Same goes when I was 70 some 16 years ago when I started looking for ways to grease My KP's. Did You ever hear of Petromatic Geasers. Screw them in the top of the KP and they have a spring loaded system of metering grease down the grease galley. Sort of worked, grease got hard and did not flow. Bottom bush did not get grease. etc. etc. 4. Or drill a grease galley down the length of the KP to the area between the bushes. I still have this system. Don't need it because of the Vesconite bushes. 5. Or drill the KP's and install a Alemite grease gun on the steering column and plumb it into the top of the KP's. Hey thats neat. Just turn the handle and grease the KP's from the cockpit. This system is on My '63 +4-4Str.
Want any more ideas. I have a million of them. Do they work? Sort Of!