Both names - Richard and Maria, and especially Richard were not uncommon in Radcliffe families. Both names were used by the Andreas family whose farm was called Belfast, and who weren't Catholic so far as I know.
Maria Radcliffe of Belfast b.1838 married William Radcliffe b.1825 of the family who lived in Ohio Cottage and had relatives in Ohio, USA.

Archd wills 1742 #42 Andreas, of Richd Radcliffe: sons Jn, James, Richd, wife Mgt Radcliffe als Quark; children are minors. [i.e.aged under 14]

There are also a number of Richard Radcliffes from Arbory parish registers listed in the IGI.

If the William you are looking for was born c.1794 there are others besides the one b.Arbory:

WM RADCLIFFE - International Genealogical Index
Gender: Male Christening: 08 JAN 1792 Andreas

WM RADCLIFFE - International Genealogical Index
Gender: Male Christening: 11 MAY 1794 Bride

WILLIAM RADCLIFFE - International Genealogical Index
Gender: Male Christening: 06 JAN 1795 Bride

WM RADCLIFFE - International Genealogical Index
Gender: Male Christening: 03 MAY 1795 Andreas

WILLIAM RADCLIFFE - International Genealogical Index
Gender: Male Christening: 16 AUG 1795 Andreas

WM RADCLIFF - International Genealogical Index
Gender: Male Christening: 01 MAR 1795 Arbory

These entries are all from parish registers.

See also: http://www3.telus.net/lawson/twill/1849_013.html
and the other wills on Brian Lawson's website.

Sue