This leaves Laois, Fermanagh, Kerry and Galway to play Mayo, Cork, Armagh and Dublin.
BBC: SPORT | Northern Ireland | The Championship | Judge Jarlath: Who will make it?
Armagh's Vinny Martin was sent-off midway in the first half before Laois' Kevin Meaney was also red-carded.
While Laois battled well against the breeze in the third quarter, Down moved into a 1-7 to 0-6 lead.
Laois started well with Tierney hitting the opening two scores of the match.
However, the game was over when Coulter nipped in ahead of Laois keeper Michael Nolan to loft the ball into the net.
Despite their opening wins over Westmeath and Laois, Donegal are likely to get a stiff test against Kieran McGeeney's side in Sunday's match (1430).
Martin was dismissed after a clash with Meaney while the Laois player followed him down the tunnel after picking up a second yellow card.
Sligo's qualifier clash with Westmeath also has a 1900 throw-in while Saturday's other qualifier between Meath and Laois has a 1800 start at Navan.
BBC: SPORT | Northern Ireland | Gaelic Games | Forde could miss Fermanagh game
John Joe Doherty makes two changes from the win over Laois with goalkeeper Michael Boyle replacing Paul Durcan and Fergal McNulty replacing Adrian Hanlon in attack.
Michael J Tierney hit two early points for Laois but Paul McCumiskey's goal and two Timmy Hanna points helped Down lead 1-4 to 0-4 at the interval.
If Offaly can use their Leinster final experience to their advantage, they might just shade it, but Laois will be keen to give Micko a last hurrah in Croke Park.
BBC: SPORT | Northern Ireland | The Championship | Judge Jarlath: Who will make it?
From that, it's my uneducated and rough guess that Armagh will play Cork in one semi, while Dublin will play Laois in the other, leaving an Armagh v Dublin final.
BBC: SPORT | Northern Ireland | The Championship | Judge Jarlath: Who will make it?
Youngster Timmy Hanna then came into his own with two fine points which helped extend Down's lead to 1-4 to 0-2 - although Tierney hit two Laois scores before the interval.
Laois start to get nose bleeds at this stage of the competition and just as everybody's beginning to warm to them again, they usually produce a tepid performance and limp out.
BBC: SPORT | Northern Ireland | The Championship | Judge Jarlath: Who will make it?
Laois, helped by the introduction of Brian McDonald and Billy Sheehan, fought bravely to get back into the game but they were frustrated by the atrocious conditions as a couple of efforts went narrowly wide in the wind and rain.
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