I agree with Elwyn -- your query will have better results if you know whether this family was Catholic or Protestant.
Clones Church of Ireland (St. Tiernach's) parish register transcripts, 1682-1900, have been microfilmed by the LDS Church, and partial indexes can be seen on their web site:
The batch number for Clones registers is C700681. Do a specific search for DOONANS in the British Isles, Ireland, with that batch number, and you'll see that there ARE Doonan entries in the Clones church records. I don't know if your James Doonan remained in Ireland to marry and have children, but you might find his marriage and children's baptisms/christenings in these Clones indexes.
However, not ALL the entries in every Clones Church of Ireland register are in this index. The original church records are housed at the RCB Library in Dublin, where you can view them (or have a local researcher look at them for you). If you're serious about finding your ancestor's records at Clones, I'd certainly follow up that research avenue.