New York started with four homegrown players and that inexperience showed as Marren went about dismantling their ambitions.
Indeed Sligo started with three championship debutants, centre-back Mark Quinn, midfielder Shane McManus and impressive centre forward Pat Hughes all lining out while veteran Eamon O’Hara was an unused sub.
Two goals from Coen and another from Hughes made the scoreline as one-sided as it looks and after the visitors recorded seven early wides, they found their stride with points from all over the park.
Marren opened the scoring after nine minutes and followed it up with a free a minute later.
In the 12th minute, his miss-kick was dropped by Armagh-born keeper Alan Hearty and the ball fell to Coen who rifled a great strike to the net with his left foot.
New York rallied and a CJ Molloy free got them off the mark but by the 20th minute, Marren had Kevin Walsh’s men 1-5 to 0-1 ahead with two more well-taken points, the second of which was assisted by Hughes who would have to wait until the second half before getting his name on the scoreboard.
As the game lost its initial intensity, Sligo kept the scores ticking over, two points from Coen book-ending a point from wing back Paul McGovern while Eoghan Carew and Molloy scored for the hosts, making it 1-10 to 0-3 at the break.
Although Carew’s free made up for a Molloy miss at the start of the second-half, New York spent most of the remainder of the game chasing shadows as a strong sun cleared the early cloud cover.
A Tony Taylor point was followed up by two frees from excellent corner forward Mark Breheny and then in the 50th minute, Alan Costello sent over a free from long distance that drew large applause from the roughly 3,000 crowd.
Even captain Ross Donavan, who had a stormer at left corner back, got in on the act while a Marren free was his final act before being substituted with six points to go with his enormous contribution in support play.
The game was long over by the time Hughes goaled brilliantly in the 63rd minute but there was still time for Coen to add his second as he skilfully rounded the keeper to slot home from 15 yards out.
Sligo now face Galway or Roscommon in the semi-final in five weeks while New York must lick their wounds and wait another year.
Scorers for Sligo: Coen 2-4; Marren 0-6, 2f; Hughes 1-1; Breheny 0-3; Donavan, McGovern, Taylor, McManus, Costello (f) Mullen and Egan all 0-1.
Scorers for New York: Carew 0-3 (3f), Molloy 0-2 (1f); Kelly 0-1
SLIGO: P Greene; N Ewing, N McGuire, R Donavan (capt); C Harrison, M Quinn, P McGovern; T Taylor, S McManus; B Egan, P Hughes, A Costello; S Coen, A Marren, M Breheny.
Subs: E Mullen for Taylor (56); J Davey for Harrison and D Maye for Marren (both 58);
K Cawley for McGovern and J Clarke for Costello (both 64).
NEW YORK: A Hearty; P Lambe, D O’Dwyer, R McGinley (capt); C Hogan, Sean Kelly (Leitrim), C Short; MJ Kennedy, E Carew; S Kinahan, E Hogan, S Hogan; D Reilly, CJ Molloy, D Moore.
Subs: M Kennedy for Kinahan (28); C Conlon for S Hogan (35); S Stokes for Short (42), Sean Kelly (Kerry) for E Hogan (45); R Stafford for Reilly (45).
Referee: Eddie Kinsella (Laois).