The surname Spelman/Spellman, the Irish form of which is Ó Spealáin [sometimes anglicized as O'Spillane] originated around what is now County Sligo. Swineford is fairly close to the Mayo-Sligo border, so it could make sense for you to have connections in that area.
Ballinasloe is 40 or so miles southeast of Swineford. Another Irish name, Mac Spealáin, which was usually anglicized without the Mac prefix as Spillane, Spillan, Spollan, or Spollin, originated in what is now County Offaly. Ballinasloe is not very far from Offaly, so that might make Ballinasloe a more likely place to search, although that name was not usually anglicized as Spellman.
The Catholic parish of Ballinasloe straddles the border between County Galway and County Roscommon. The parish records which are available online go back to 1820, which is pretty good for that area, and you can access them at this link:
https://registers.nli.ie/parishes/0324
The Catholic parish of Swineford/Kilconduff in Mayo has records going back to about the same time (earlier for some marriages). You can access them at this link:
https://registers.nli.ie/parishes/0133
Without more info (such as his parents' names), you may have to simply search the parish registers, but at least they do go far enough back.
You may already be aware of them, but there are records for Michael and Hannah in the FamilySearch database [https://www.familysearch.org]. If you search there, you can find Michael under ID number GVQ1-3LK, and can access the records for the others easily through that record, as you will see. There is no further Irish info there, but in each record, at the right hand side of the screen, you can see the screen names of those who have created or modified the record, and can send them private messages, so you might be able to get more info by contacting them (and perhaps also locate some relatives that way). Perhaps they have more of an idea as to where to look for baptismal records.
