I wanted to do an update on this as I think that NY has more SP prospects than people generally give them credit for, and also a lot of the guys above have moved up a level or two in the last few months:
Chad Green, Luis Cessa, Dietrich Enns, Brady Lail, Jordan Montgomery-AAA
Chance Adams, Ronald Herrera, Daniel Camarena, Domingo Acevedo (hasn't yet pitched in AA but was about to be promoted when he hurt his back last week)-AA
James Kaprielian, Justus Sheffield, Josh Rogers, Ian Clarkin-A
The biggest prospects there are Sheffield, Kaprielian (hurt), and Acevedo (also hurt), but all five guys at AAA currently look like big league pitchers in some capacity. Chance Adams has had an amazing season, his numbers and Enns' numbers have to be seen to be believed. Herrera has had an OK season, but is one of the youngest players in AA still. Rogers also is having a great season, a 2015 11th round pick who has been great in both low A and high A, a 2.30 ERA combined in 113 innings.
Also we're still waiting to see who Cashman gets from PIT for Nova, my guess is that will be two more SP options. And I didn't include Dillon Tate until NY has him starting games again.