Hi,
It seems James and Eleanor were married in 1840 (see attached) and they had children John (1841), Peter (1843) and James (1845). The parish records didn't start until 1839. Although there may be a few marriages in Mayo in the 1820s, I couldn't find a record of a Carter marriage (that is, no record of James' parents).
Hope this helps.
Best wishes, Kieran Jordan