I do this drive from Donegal regularly and find this to be the best route to North Dub. (As caveat says, depends on where you're going to in Dublin.)
Omagh, Aughnacloy, Emyvale, Monaghan, (bypassed)Castleblaney (bypassed), Carrickmacross (bypassed), at Ardee roundabout take exit to M1 and then M1 all the way into Dublin.