Dai,
Where are you?.. geographically wise that is.. This will undoubtedly affect your choice of repotoire...
A couple of good English Morris Songs are The Nutting Girl (the usual folk subject of sex) and The Postman's Knock (another good folk subject of marital dischord).
I take your point that you are and wish to remain unaccompanied, but as LEJ hinted at, if one member of your troupe is or could be competent on the Bodhran.. Whiskey Your The Devil is a great number to do (along with a thousand others)
Cheers
Mick