OK guys, bear with me a moment or two.  I very quickly scanned the Yankees and NYCFC schedules (emphasis on "quickly", so don't hold my feet to the fire if I missed one or two) to see how many conflicts will arise concerning YES telecasts this season.
Here's what I came up with:
--Saturday, 4/11:  Yankees vs Boston, 1:00 start........NYCFC, 4:00 start.  Not too much of a problem with this one and with it being a Saturday there is always the chance the Yankees-Sox could be moved to a national broadcast.
--Saturday, 6/13:  Yankees vs Baltimore, 7:15 start.......NYCFC, 7:00 start.  Problem.
--Saturday, 6/20:  Yankees vs Detroit, 7:15 start.......NYCFC, 7:00 start.  Problem.
--Thursday, 8/13:  Yankees vs Cleveland, 7:00 start.......NYCFC, 7:00 start.  Problem.
--Saturday, 8/29:  Yankees vs Atlanta, 7:00 start.......NYCFC, 4:00 start.  Shouldn't be any problems here.
--Wednesday, 9/19:  Yankees vs Tampa Bay,  7:00 start.......NYCFC, 7:00 start.  Problem.
So unless I missed one (don't think I did, but please feel free to double check) there's 4 major conflict the entire season.  The 4/11 game may be delayed until the Yankees-Sox game ends (which would suck, but remember that game could always be moved for national viewing) and NYCFC should be well finished on 8/29 so the Yankees could come on at 7:00.