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I did some searching on the subscription site Roots Ireland and found this William King death record in the Boyle Church of Ireland records. I thought I would share in case you may think it is your William.
Name:WilliamKingDate of Death:08-Nov-1847
Age:57Parish / District:BOYLE-CHURCH OF IRELANDAddress:BoyleCounty:Co. RoscommonStatus:
Denomination:Church Of Ireland
Like you I found three baptismal records for children of William King and Letitia Minchin. Thomas 1837 Sarah 1838 Antony 1842
Emlaghfad and Eastersnow do not border. My thought is that William King met Letitia thru a social circle and they decided to mary and the marriage was in her church but after the marriage they moved back to Ballymote.
Let me know if you have any questions.