John and Annie appear in the 1930 census of Akron. It shows he immigrated in 1870 and she in 1882.
The 1920 census of Clearfield County, PA shows he immigrated in 1880 and she in 1883.
The 1910 census of same shows he was born in PA but nevertheless immigrated in 1882. She immigrated the same year. The surname is misindexed as Gilray.
The 1900 census of same shows he immigrated in 1869 and she in 1882. They were married 10 years.
There was a John W. Gilroy who immigrated in 1869 of the right age with a father named William, but there was also another John W. of the approximate right age who immigrated in 1881 with his father William. It's possible they are the same people and immigrated more than once after going back to England.
Some of these records you can look at for free at beta.familysearch.org and Ancestry.com. For those you cannot see for free I suggest checking with your local libraries to see if they have Ancestry or Heritage Quest.
You can look at John W. Gilroy's 1939 Ohio death certificate for free at: https://beta.familysearch.org/s/collection/show#uri=http://search-api:8080/searchapi/search/collection/1307272&hash=Mrd8SMocDIIen2Q83tu%252B82PRagg%253D (you'll probably have to cut and paste this to go to the website)
It shows he was born in Yorkshire and his parents were William G. Gilroy and Mary E. Maven. You'll probably have to go to the Ohio Dept of Health to look at Annie's death certificate.
At this website you can look at the data on the July 30, 1865 marriage of William George Gilroy and Elizabeth Mary Maven in Durham, England: https://beta.familysearch.org/
With a bit of searching you can probably find more.
You could also try to get John and Annie's marriage record. They probably got the license at the Clearfield County Register of Wills. It may have data on her parents and where exactly she was born. Her obituary would probably be helpful and I imagine she's buried with John.