I’ve used one called Uniplaces in Lisbon. They operate in large parts of Europe. Despite the name they are open to non-students as well (they call it “young professionals”). Only allow rentals of 28 days or longer. They do charge a fixed service fee per rental meaning it’s the same if you rent for one or six months, making longer rentals better financially.
Protip: Use the coupon “UNI9E69001” for 25% off their service fee.
EDIT: The above coupon seems to no longer work. You can use my personal referral code (UNI82275462) for a measly 10% off, or search Google to see if you can find any better ones.