The NY Petitions for Naturalization Index has a William Doogue age 38 living at 600 E 167 St in the Bronx in 1933.
In an actual petition for a William Doogue from 1931 also available on Ancestry.com, he gives the same address, says he was born in Tarnano, Ireland on 26 Sep 1895, and is a roof driller. He says he married his wife Margaret on 5 Nov 1932 in the Bronx. Margaret's birthday is given as 10 Sep 1897 and she immigrated in 1911. Witnesses are Winifred McDonough and Thomas Sherlock. This document is dated 8 Aug 1933.
A William Joseph Doogue born 9 Sep 1894 in Queens Co., Ireland shows up in the WWII draft cards. He wrote his address as 600 E 167th St in the Bronx (see above) and someone crossed it out and wrote either 2955 or 3955 Decatur Ave, Bronx, NY. He is supposed to list the name and address of someone who will always know his address and he lists a Mrs. Margaret Doogue but does not give her address. He lists his employer as the WPA.
The NYC Grooms Index (
http://www.italiangen.org/nycmarrigesearch.asp?code=6) says that a William Doogue married Margaret McDonough on 5 Nov 1932 in the Bronx (certificate #7598).
Perhaps he is the right man?