I am not sure it is a match, but could be. Was your William Swearingen married to a Susan Baker??
I have found a Bridget Cunningham married to Robert Cunningham on the 1885 Nebraska State census. She is 23 years old and born in Pennsylvania. The age is right, and she is near Omaha. I have not seen the original census just the abstract on Ancestry.com, and I haven't checked for a death record of Robert Cunningham. As soon as I have time I plan to check that out.
There is also a William Swearingen married to Susanna listed on the 1880 census (and 1870 census) in Richland, Wyandot County, Ohio. The names and ages are about right -- but there is no daughter named Bridget listed.
Someone else has done researching on the Swearingen family listed above on the Ohio census. They have Susan's maiden name as Miller. And again no Bridget listed.
So nothing fits exactly for the Bridget Swearingham/Cunningham/McCourt I am looking for. If I find any other information I will post it and let you know. Thanks. Kathy