What friends of mine have done is found somewhere and then said 'oh, the dog's ok, yeah?' when they're handing over the deposit and first month's rent. Landlords are a lot more amenable to pets when you've a big wad of cash in your hand. You could also offer an extra sum as a pet deposit and/or references from your old housemates and neighbours about the dog's behaviour; the landlord will worry that it'll chew everything, pee all over the house, and annoy the neighbours, if you can guarantee that won't happen (as much as one can guarantee those things) you shouldn't have a problem.
Generally though, with so many people moving for work and due to mortgage problems, there are more people looking to keep their animals, so the landlords seem to be getting more accomodating.