I'm looking for slang words that would have been in use around 1910 in New York. Anyone know of an online resource that might work?
Green's Dictionary of Slang is a highly regarded and well-curated dictionary that I would feel safe calling "the best online slang dictionary" in a holistic sense. The website is easy to use, and
with a paid subscription you can access its massive collection of citations, now available for free without a subscription.
Even with GDoS, the granularity is not to the level of "New York." You could search for words or senses formed in the U.S. between 1910 and 1919, and optionally specify cultural context in searching, but if you really want to find slang unique to New York in 1910, you might consider seeking out texts that were published around that point in spacetime, or sociological works specific to that culture.
I suspect your best bet will be to find a print slang dictionary contemporary to your desired time period. Fortunately, many of these will be out of copyright and therefore available online. Google Books is a great way to find these (under "Tools" you can limit your date range to something that seems sensible), and you could also look in Project Gutenberg or Hathi Trust's Digital Library.
One example is the 1896 A Dictionary of Slang, Jargon & Cant Embracing English, American, and Anglo-Indian Slang, Pidgin English, Gypsies' Jargon and Other Irregular Phraseology (link is to Vol. II). It's a little earlier than 1910, but some of the phrases labelled "American" would probably still have been in use fifteen years later. Entries are labelled with region, including some that are specific to New York and others that are more generally "American". A sample entry:
Swartwout (American), a verb of local (New York) origin or usage, signifying "to abscond," "to vamoose," "to skip." A Mr. Swartwout once decamped from that city, carrying with him a large amount of public money—hence its origin.
This dictionary and a few others very tantalizingly cite a New York Slang Dictionary, published by R.K. Fox, which I believe is Alfred Trumble's A Slang dictionary of New York, London and Paris : a collection of strange figures of speech, expressive terms and odd phrases used in the leading cities of the world, their origin, meaning and application / collected and arranged by a well-known detective ; containing portraits of celebrated criminals, with sketches of their lives. (1880; access via Hathi Trust.) The entries aren't labelled with origin, as Trumble's thesis is that "thieve's patter" is exactly the same all over the world(!), but he appears to have done most of his actual collecting in New York City so it may be useful to you.
If you're just looking for a manageable collection of slang words and phrases that were probably in use around 1910 in New York City, you could do worse than the glossary of terms in Life in Sing Sing by "Number 1500," published in 1904. Since Sing Sing prison is located just 30 miles north of the city, its slang undoubtedly is and was strongly influenced by city slang.
Number 1500 very conveniently sets aside 15 pages near the end of the book (pages 246–260) for a "dictionary of thieves' and convicts' slang." I can't vouch for the contemporaneity of all of the entries (compilers of slang dictionaries in centuries past had an unfortunate and unscholarly tendency to simply reissue older slang compilations under their own names or to fill out their own efforts with cribbed entries of dubious currency from earlier dictionaries), but many of the ones in Number 1500's glossary seem to be on point and reasonably up-to-date.