Some more interesting tidbits. Since you knew his date of immigration, I'm assuming you have already seen his New York arrival in 1883. If not, let me know.
I found him in 1900. It is so him...he's living in a boarding house and he's a clothing salesman. He's single, gives DOB as Dec. 1858 (his death certificate says his year of birth is unknown, but he was born Dec. 30). The census says he was born in Texas but his parents were born in Ireland. Interestingly, the landlady at the boarding house is Mary Mellinger. She's not Irish...her father was German and her children's father is listed as born in Germany. Weird, huh?
But here's the real useful information. Turns out he and Margaret went on a ship from Galveston TX to New York City in 1929. They are listed on the immigration form of US citizens. He's 71, she's 45 (born Sante Fe, MO on June 10, 1884). He's listed as born in Ireland. The good part, however, is that he was naturalized in the District Court in San Antonio in 1896. There may be records available on that and it may have place of birth.
Finally, I did find a Mellon in County Limerick. Gar seems to be a Gaelic word. You may want to check that out.
Anyway, good luck! Hope this helps! Bon Voyage! Andrea