Welcome to RC brisbanegirl
Do you have any further information to help in searching?
for example the date of marriage, his father's name (usually on a marraige certificate), date of immigration, etc.
There are quite a few possibilities on the 1901 census in Co. Leitrim and he also may have immigrated before that.
Editted to add:
There is a New York War record dated Jun 5th 1917
It states that this Patrick McGOWAN was from Co. Leitrim, aged 29 and single
If you know the date of his marriage you could see if this is him
He gives his date of birth as Dec 08 1887 crossed out to read 1888
His address was 885 3rd Avenue, New York and he was employed at W J Taylor, West 67th Street
There is just one birth in Dromahair that I can see around that time but be wary as many records are not online and the catholic baptisms for Dromahir only go to 1879
But date is Dec 1887 to Patrick and Honor BYRNE
There are other Leitrim births but not in Dromahair
