Barbara,I was looking at the census and found the following.
1930 US Census; James Toner age:35 status:roomer with Qualey family(misspelt in census) born:Ireland parents born:New York single
in the 1940 census;
James Toner head of household age:39 born:Ireland @ 1901 married naturalized living @ N.E. 136th street Julin(?)(poss Julia?)Toner age:38 born:Ireland @ 1902 married wife naturalized Hugh Toner age:20 born:Ireland @ 1920 single son James Toner age:17 born:Ireland @ 1923 single son *info on the 1940 census was given by son James Toner
I then looked at marriages in Ireland for James and couldn't find any nor could I find definitive births for Hugh and James Jr.I do believe that the 1940 census is your James who was with Qualeys in 1928 & 1930.I could not locate wife and sons on passenger lists between 1930-1940 but they may have been in US before this.I would definitely get a copy of his naturalization record as well as look around to see if perhaps there is a record of divorce.If you have anything more I will look further.Hope this helps,Kim