I've never done a goose, but when I do muscovy drakes, which are the biggest critters I feel up to dealing with, I have a chopping block near a tree with a noose set up tied to the tree trunk. I use the noose to keep the duck's head roughly in position so I get a good swipe with a hand axe, which is as much as I can manage when I have a critter in the other hand.
Here's a photo of my current set-up so you get some idea what I mean.
You can just about see the loop of black baler-twine around the lower part of the trunk, and if you look closely there's head (in a sock - I'm a coward) to the right of the chopping block.
The block is a bit of oak, sawn along the grain so it doesn't keep splitting when I whack it with the axe. It's cut quite long to allow for the length of the neck and the fact that I want the main body well supported. I keep more baler twine on the branch of the tree so I can hang them to bleed out.