Two years ago there was a very complete auction of coins from Balearic Islands. The catalog of the auction is a good book for Balearic coins. You can find it here:
https://www.aureo.com/mediaaureo/Subasta0272-1/catalogo0272-1.pdf
You can see some medals minted in Mahon in XVIII century, but under Spanish rule.
The main reference for Balearic coins is Numismatica Balear by Campaner. You can find the scanned book. No reference to any other coin in Menorca in those years, except the medals from Mahon.
I figure that the coins used under English rule were the Spanish and English of those years. The coins used by common people everyday were doblers, and the garrison would use pence.
https://en.numista.com/catalogue/pieces109204.html