No information has been posted online or released in any way publicly about if there will be a third season of "NY Ink" on TLC. TLC has not released an official statement yet. But, it's considered very likely, as its predecessor "Miami Ink" lasted 6 seasons and the other spin-off, "LA Ink," lasted 4 seasons.
Another reason to be optimistic is that the second season just ended on March 1, 2012, so it hasn't been long since it stopped airing. Also, it was only about 5 months between the first two seasons, which shows that the series is in relatively high demand. So, it may be a few months, but it's very likely to be back.
All of Season 1 of "NY Ink" is now showing on Netflix Instant, and episodes of Season 2 are still available to watch on Verizon FiOS On Demand.