Just about every British printer of broadsides printed it, from the late 18thc onwards. Almost all versions mention Pomeroy (Co. Tyrone) in the first line. I haven't got any early Irish printings but no doubt they existed. The normal route for such material was originated in Ireland (often the north) and brought into England via Liverpool and dispersed from there northwards and southwards and fairly soon across the Atlantic.. The earliest version I've seen is titled 'Rinordin, or The Mountains High' (British library).

Early 19thc versions were printed by Nathaniel Coverley of Boston and then by the 1840s in such as The Forget-me-not Songster, but still with Pomeroy as the setting.

The above suggestion is somewhat bizarre!