John is exactly the right age for the John Murphy who was raised by the Mulvaneys.
According to Betty and John, the Murphy brothers had two older sisters, one of them named Annie. I'm hoping that Any is Annie and not Amy, or else this is probably the wrong family. Amy, while it sounds to my ear like a very modern name, was actually the 120th most popular name in America in 1887, the year this "Any" would have been born. (The supposed modernity of Amy comes from its extreme popularity in the 1970s, when it was the #2 most popular name for 4 years running.) Annie, of course, was at #12 in 1887, and Ann and Anne were also very popular, at 124 and 121, respectively - the real popularity of the name is disguised by the fact that the two variant spellings were almost equally popular, making the name that sounds like "Ann" twice as popular as the rankings would suggest. Though the ranking of Amy is similar to those of both Ann and Anne, there were 251 babies named Amy in 1887, and 488 named either Ann or Anne, which is more in line with the numbers one would expect of a name ranked in the 70s in that year. Add in Anna at #2 (4,227 births) and Annie at #12 (1,844 births) means Ann- names were much more popular than Amy, and more likely to be encountered when looking at this sort of demographic data.* But "Any" could still be Amy, and, as much as I want this to be the right family, I do think that "Any" is more likely to be a "typo" for Amy than for Annie.
So on the name count, I'm not committed. Is "Any" Murphy our Annie Murphy Dowd? Dunno.
Something I do find particularly interesting, and potentially indicative of this being the right family, is Thomas Murphy's occupation. He's listed as being a coachman. As you'll recall, William Toner's death certificate listed him as a stableman, and in 1889, a news item referred to a William Toner driving a coach that was "the property of Mr. Murphy, of South Brooklyn." More than anything, the occupation - and the right birthdate for John - makes me think that these are our Murphys, that Mary A. is Mary Ann Toner Murphy, and that William Toner was working for his brother-in-law when he was involved in that accident.
*Source for name data: The Social Security Administration: http://www.ssa.gov/OACT/babynames/