After talking to a couple of guys at work who have rented out properties, they would gladly pick up dog poop for someone who is otherwise responsible and PAYS THE RENT.
I have been on both sides of these types of rentals, as landlord and tenant.
If I were your tenant, I would pay for your maintenance of your yard and you would NEVER see a single turd. Landlords like you are rare.
It is very hard to rent with a pet, I know well firsthand, the landlord must charge accordingly.
I was a landlord and I accepted pets. # 1 rule, always get a big NON-REFUNDABLE deposit PER ANIMAL. #2 min one months deposit no exceptions (you will need it to repair the damage from the animal) #3 there will be damage carpet, urine on walls etc, always deduct from the deposit.
It's a lot cheaper than finding a new renter.