I started with this recipe: http://www.aveganchef.com/vegan-baileys-irish-cream/ - basically because I came across it first on Google. However, that recipe uses coffee, which seems wrong (well, OK, coconut milk is also pretty wrong, but let us move on from that). Bailey's is not flavoured with coffee, but with vanilla and chocolate.
So, what I did in the end was:
1 can light coconut milk
1 can full-fat coconut milk
100g soft brown sugar
about half a small mug of hot chocolate, made with hot water and 2 dessert spoonfuls of cocoa.
2 teaspoons of vanilla extract
Boil all those things together on a medium sized pot for about 10 minutes, and let it cool a bit
Add about a small mug Jameson Irish Whiskey (vegan) and give it a good stir.
This made enough to fill a bottle (which had contained Pimms) and a jar. I intend to try the stuff in the jar tomorrow once it's fully cooled, and report back on whether it's actually drinkable! It looks a bit dark in colour - possibly I should have used a paler sugar, or less cocoa.
ETA later: This produces a pleasant enough coconuty sweet liquid, but I found it a bit harsh to drink on its own, and so have endded up pouring it over things. It also separates out like nobody's business. Probably won't be doing this again.