Jitney routes started as a form of entrepreneurship. Drivers started their routes, and if there were enough passengers, keep providing the service. However, there have been some times where attempts to start a route have failed. Since there is no record of when these services were offered or withdrawn, I can only present my own anecdotal evidence.
Greenville (Jersey City) – New York : Once in about 2015 I saw a piece of paper, taped up to the door at Gate 51 of the Port Authority advertising this trip. It was once a day, leaving at 5:45pm. There was a phone number listed. I called the phone number and there was no answer. I assume this was an attempt to start a route, but it did not work out.
Paterson Market Street – Route 46 – Teterboro – Union City – New York:
I spotted a sign for such a route, on a bus dropping passengers off on 40th Street, near the Port Authority Bus Terminal, in December 2017. The driver said that the sign was not accurate and he did not come from this route. I have not been able to find any other information other than this one occurrance.
This route was once run by Community Lines, who run the Kennedy Blvd – Port Authority route. It ran less than hourly, and was discontinued some time in 2016. Click for more details.