Coulter was a native of Glenariff, County Antrim, in what is today Northern Ireland.

[1] In the late 1870s, he went to Europe to study with marine artists Vilhelm Melbye, François Musin, and J. C. Jacobsen.

[3] Coulter resided in the San Francisco Bay Area until his death on March 13, 1936, at the age of 87, in his Sausalito home.

The SS William A. Coulter was a Liberty ship which was constructed and deployed in 1943, and named in his honor.

[5] In 1923, the United States Post Office issued a commemorative 20-cent stamp with one of Coulter's paintings.