Christine,

The earliest census on the island was taken in 1841, so no luck there. There were manorial and rent rolls taken at various times, but these may not be very helpful without knowing the parents.

As for immigration records, no. You might have luck searching passenger lists, but those too are hit and miss. You might consider a visit to the National Archives, or you could write them with the details. For info on how to do this: www.genealogy.com/24_myra.html.

The Manx prior to 1790 were primarily members of the Church of England, although there were small pockets of Quakers, so doubtful you'll find anything useful trying to chase an Episcopal connection to the island prior to that date.