Novedades has more and better rentals than other newspapers. But the best way is to poke around in neighborhoods that you want to live in, looking for signs. I would NOT recommend renting a place sight unseen. I think it's your doggies that might have an issue adjusting to the moist heat. My dog grew up in Cancun but now that he's older, I would not want to bring him back to live there as I think that acclimating would be really tough. I also love your idea about doggie care. I would have loved a nice, trustworthy place to leave the dog when I visited the US...also, I'd like to see pick ups and drop offs included! It was always frustrating asking for rides to the get the dog to the vet and I really appreciated that mine did pick ups (for surgeries) and home visits (for vaccinations).
Robbie: Like gbchayctca says, scouting around a neighborhood is by far the best way when it comes to finding rents. There are literally thousands to choose from - for rent/for sale signs are everywhere. Central might not be the best if there are plans to have a "doggy day care"-thing going on, mostly due to the previous mentioned airheads.
If you want to live between Playa and Tulum as initially suggested then there isn't to much to choose from. Your best bet would be renting something in Playa, that way you'd be close to schools, stores and doctors etc. You can rent a house on the "other side" of the highway, not the beach side, with a small bit of land for 6500 or so. I'm guessing you need to be close to civilization for the business? or is the breeding etc all done with online contacts? You could also choose Tulum and rent something with a bit of land for quite cheap (although it's not gonna be that nice) but I'm guessing you've got your expectations in line if you're looking at 5000 rent a month. Good luck I hope it all works out great for you.