A tenor is a tenor and the usual tuning for "Irish" is EADG (or GDAE as I call it). Working my way, the instrument are normally tuned CGDA for Jazz and for some reason most string makers do not seem to have caught on to this and only make the CGDA sets.

If you are looking in a store for an "Irish" tenor, I think that you really need to try them strung with strings suitable for the GDAE tuning (heavier than the others) to get the full impresion as to whether you really like the instrument or not but depending on where you live, you may just be lucky to see a tenor.

Jon