If you really only need the car once a week, I would consider just renting one from one of the dozens of car rental agencies in the POP area. Most of the major car rental companies have franchises and there are several "mom and pop" operations. You could probably work out a discount from the regular daily rental rate based on the consistant business. You could do this for years for less than a cheap used car would cost.
With that money he would spend at a car rental he could also just hire a taxi driver for the day.
I know a very good guy who will give you a decent deal for a weekly rental, especially if its every month for 6 months. A friend of mine had this same arrangement with him. He has a couple of decent Suzuki Gran Vitaras he rents. If you're interested, PM me and I'll send his info. He's in Cabarete but can meet you in POP...
The OP doesn't want one week a month. They want one day a week.