For Win(ifred) Noon B 1818 (exact) somewhere in Ireland with a father's forename Pat(rick), I found 0 B rcds. The closest rcd matching your criteria is a Winifred B 1825 in Co. Roscommon. This may be too late for your timeline. You can validate this by viewing the detailed rcd to see if the mother's name was Ann.
For Winifred Noon M 1839 +/- 4 yrs somewhere in Ireland, I found 3 M rcds: 1836 Roscommon, 1837 Mayo, and 1839 Galway.
For Martin Whyte/White ditto, I found no matching M rcds for those of Winifred. It may be they married in one of the counties where rcds haven't been transcribed.