Ditto to justin’s advice.
Evidently your asking rent is too high. You’re attracting the folks that are being turned down elsewhere, and are less concerned about the rent, than they are about smoking and possessing aggressive dogs, and paying their bills on time.
We have a 25lb limit on dog size, wherever we allow dogs at all.
If it’s legal in your area, you could simply ask for three or four times the contract rent in deposits, and charge the rent you’re quoting, but only with a 24-month lease.
This way, you’re getting top rent; getting it for at least two years; and you’ve got a big enough deposit to cover quite a bit of damage.
Tenants rarely walk from large deposits that are ‘large enough.’ They will work to get them back, including maintaining the place, and cleaning things up on their way out.
At the same time you need a hefty late fee that you’re willing to enforce.
You could also ask for a co-signer.
Or you could lower the rent until you start attracting the bargain hunters with good credit, residence histories, and income requirements.
As Justin suggested, put a sign in the yard. List the rent and your phone number.
The most likely prospects for your rental are already trolling the area.
To better gauge the rents, call other landlords in your neighborhood with similar units to rent, and see what they’re asking. Also search Craigslist for similar sized units/houses in your area, and see what their asking rents are.
The most accurate feedback will come from the responses to your well-placed ads (especially the front yard of your rental house).
Hope that helps.