Thanks to those who responded to my query.
I got the references from an obituary in "Y Cyfaill o'r Hen Wlad" in 1866.
(For John Davies and his wife Jane, of Paddy's Run, Ohio, who had both died
of cholera.) It said (translated) "they were originally of Llanddewi
Aberarth, Cardiganshire......married in 1827.....and became members of Eglwys
Crist with the T.C. ["gyda'r T.C."] in Llan Onn".
I can't work out what T.C. means (can anyone help there?) I took Llan Onn to
be the same as present day Llanon, but in view of what Gareth says about
there being a Llansanffraid Llan-non maybe that's what was meant. (Is it the
Llansanffraid which is the next village to Llanon?).
All detective work appreciated :)