Preventing discoloration when making fresh mint liqueur
Idea 1:  Assuming the leaves are oxidizing: you could add an antioxidant.  Vitamin C is handy and will scrounge up oxygen radicals.  Crush up some pills and shake them in.  It will make it a little sour too - ascorbic acid is vitamin c.

Idea 2: deplete your alcohol solution of dissolved oxygen first.  When you heat something to near boiling, the first wave of bubbles is gas coming out of solution.  Do that with your alcohol.  Add it steaming hot to your steeping vessel (maybe heat up vessel first with warm water so it doesn't crack!), put in mint and then cover it airtight.  Maybe that will exclude enough O2 to keep things green.  Also would serve as the blanching step in linked article.

I was pleased to see the vitamin C idea was listed in the linked article about keeping pesto from turning black.

https://www.thekitchn.com/good-question-w-4-12832

Pesto is made with basil which is a mint so the same issue as you have.  The other recommendations from that article are blanching the basil (yah!) and adding lemon juice (vitamin C!).