I searched the Irish Family History Foundation's database. It contains 11,500,000 surviving rcds for abt 60% of Irish counties. Rcds B4 1840 are sparse. I had mixed results.
For both William Stapleton and Winifred O'Bryne M 1823 +/- 4 yrs, I found 1 M rcd for Wm, 1819, Co. Roscommon, parish of Aughrim and 1 M rcd for Wn, 1819, Co. Roscommon, but in a different parish. These name combinations are so rare that I think there is a transcription error for Winifred and/or William. Read on.
For the children, I found these DOBs in Aughrim parish: Mary: 8 B rcds 2-1819, 2-1822, 2-1823, & 2-1824 Mart: 2 B rcds 2-1821 Anne: 1 B rcd 1826 Jame: 1 B rcd 1834 Wini: 1 B rcd 1837
There appear to be at least 6 families of Stapletons in Aughrim parish during this era. A view of the detailed rcds for the children SHOULD show the parents' names. For the possible transcription error on the parent's marriage rcd, you should ask the IFHF to check their database against the actual rcds.
Google the Foundation's name to lead you to the database.