Agree with Luddite, i have 2 Wanner grease guns, the first i bought 54 years ago, the 2nd i bougnt from ebay secondhand £25. Wanner is the grease guns of choice.
You should then contact "The Nipple Shop" and source one of thier Remote greasing kits for Morgan. It consists of 2 x 2 nipple manifolds, one located on each of the inner wings and connected to the upper and lower grease points with poly tube. About an hour installation time. A great bit of kit, it allows easy greasing, you only need to lift the bonnets, great when you're touring.