Like Annie Laurie, Comin' Thro' The Rye was popularised by Jenny Lind on her 1849/50 tour of the USA. A Levy search on RYE will find you the sheet music of a number of versions from the 1850s. All the "modern" versions, as far as I know, are based on the Jenny Lind music.

As Genie says, there may well be more "anglicised" versions of the words, but there is probably not a standard one and you can do it yourself easily enough.

Cheers!
Ian