Looking for confirmed parentage of Richard Harrison of Arbory bn c 1783

There are 3 possibilities -

Richard bp 25 Aug 1782, s/o Richard Harrison & Catherine Coole

Richard bp 27 Dec 1782 s/o John Harrison & Elinor Cowle

Richard bp 14 Nov 1784 s/o Charles Harrison & Jane Cowle

He married Anne Leece in 1803 Arbory and they had 10 children -
Cath 1803, Elizabeth 1805, Esther 1808, Elizabeth 1811, Richard 1813, Thomas 1716, Ann 1819, William 1822, Ann Jane 1825.

I speculate that he may be the s/o Richard H & Cath Coole, however that is only based on the fact that they baptised their first child Catherine..... I need the proof of course....anyone researching this family?

Thank you
Elizabeth