It is a bit of a pain trying to rent when you have dogs but I first rented when I had two, and then when I had three in a different place - so it is possible.

Do you have any estates around you (as in country/sporting estates?). They often have an estate office you can apply to. Their cottages are usually old gamekeepers or shepherds cottages and they almost always allow dogs - as well as being in lovely countryside So worth checking out.

I would also check your local paper (rather than trying letting agents, as they almost always say no to pets) and ring any houses you like the sound of. Mention you would like a dog (or already have a dog) and, as K9xxb says, offer to have the carpets professionally cleaned when you move out, offer a larger deposit etc.

Also look in post office windows etc for adverts. Speaking to a private landlord is a far better bet than going to estate and letting agents.

It isn't easy, but it definitely isn't impossible - so keep at it