Do you know if the O'Boyle family were Catholic ?
You could check for parish records - but since you have quite common names, and no location your search could be very difficult. The other point to be aware of is that not all parishes were keeping records for the dates you mentioned, and very few RC parishes have records before 1800.
You can see a map of the RC parishes in the county on the Irish Times website at :
Mayo RC parishes (click on the map to see details & dates available for each parish)
Some Mayo records are available on the pay-website of the Irish Family History Foundation at
www.irish-roots.ie The records they have are transcripts, and may not include all parishes or records.
Shane