Hi Robert - Hope this is of some help. Our PERRYMAN line seems to have been based in Devon from at least early 1500s. After several years of research in Devon, I've found no mention of the name Jeremiah Perryman, or accounts of them working on the plantations in Ireland.
However, from other Perryman researchers found that there was a contingent of Perryman's in the county of Essex, England. The website below, mentions a Jeremiah Perryman of Essex, see
http://www.mocavo.com/A-History-of-Coggeshall-in-Essex-With-... Hope these websites will also be useful.
http://www.surnamedb.com/Surname/Perrymanhttp://www.nivek-systems.co.uk/genuki/ESS/http://en.wikipedia.org/wiki/Plantations_of_Irelandhttp://en.wikipedia.org/wiki/Plantation_of_Ulsterhttp://en.wikipedia.org/wiki/Walter_Devereux,_1st_Earl_of_Es...(mentions the Plantations of Ireland)
Hope it helps. Sue