When the diocese sent a list of possible candidates for bishop to the Vatican, Cosgrove's name, despite being vicar general, was missing.

[5] Cosgrove was appointed the second bishop of Davenport on July 11, 1884, by Pope Leo XIII, and was consecrated in St. Margaret's Cathedral on September 14, 1884, by Archbishop Patrick Feehan of Chicago.

[2][3] Bishops John Hennessy of Dubuque and James O'Connor, the Vicar Apostolic of Nebraska, were the principal co-consecrators.

[6] Cosgrove was a friend of Archbishop John Ireland and was aligned with the more progressive wing of the American hierarchy.

While the diocese had no newspaper at the time, the periodical Iowa Orphan's Friend reported on Cosgrove's activities and published his pastoral letters.

In 1903 he was quoted in the national media calling Davenport "the wicked city of its size in America" because of its notorious Bucktown District, an area of speakeasies and brothels that was close to St.

[10] On October 7, 1904, at Cosgrove's request, Pope Pius X named Reverend James J. Davis as coadjutor bishop of the diocese.

Cosgrove was the first native born bishop of the United States appointed to a see west of the Mississippi River.