Hooligan appeared in the 1890s in New York, and also in London. There are three postulated sources. Take your pick.
1. From Hooley, or Hooley's gang. A misunderstanding of that name led to hooligan. Reports of "hooligan" gangs in the London papers.
2. Hooligan gangs in London; the name from a "Patrick Hooligan", a bouncer at the Lamb and Flag pub, who had a gang and who died in jail after murdering a policeman.
3. Hooligan figured in a music hall song of the 1890s about a rowdy Irish family. Information mostly from the OED.
1902- Character song, "Happy Hooligan," pub. in the music supplement of the New York American and Journal (Can be seen on line in the Levy Collection).
Hooley, a not uncommon surname. The Hooley Minstrels performed in the Civil War period.   

Larrikin- 1882, in Jago, Ancient Language and Dialect of Cornwall: "Mischievous young fellows, or larkers."
1868, Harper, in Letters from New Zealand: "We are beset with larrikins, who lurk about in the darkness..." The earliest in print so far found.