You just don't tell them you have any pets. Normally the landlord doesn't come to your house once you're living in it, at least from our experience they don't. If the house needs repairs, they send out someone to fix things. If/when they do, you can just put away all signs of pets, and while the repair work is being done, just take your pets in a vehicle and go out for the day, or hide them in rooms the repairman doens't need to access. If you have barking dogs, then yeah, drive them to a park for a few hours, and hide their water and food bowls, cat litter boxes, etc. We are living in a place now that only allows for 2 pets, and we have 5 cats, 4 big dogs, and 3 kiddos. Ha! Good luck.
Oh, and we are in the process of closing on our house in SE Portland (Mount Scott near the Clackamas Town Center) in the next week or so. If anything falls through and we're forced to rent it out, I could always contact you. It has nearly .5 acre fenced-in back yard that backs up to acres of forest of the Willamette National Cemetery. Nice view of Mt. Saint Helens from the kitchen window and wrap around porch.