Shaving downstairs is easy with the use of an electric shaver and a mirror for reference. Keeping hair from growing back is nigh impossible and all dependent on how hairy you are to begin with. I'm a fairly hairy individual, but my body hair grows back at a snails pace compared to my facial hair. If I shave downstairs it takes usually 4 weeks or more for it to grow back to the point at which I have to shave it again. I have heard that if you shave or keep things trim regularly you can prevent it from growing back at a regular rate.
As others have said, waxing is certainly an option. I had a friend who waxed parts of his body and it took months for the hair to begin growing back. Waxing however has a few major drawbacks, for one thing it's a painful process and secondly, it can lead to impacted follicles and ingrown hairs. For that second reason alone, I've never considered getting a wax.
As ESPF has pointed out, the only surefire way to remove hair and prevent it from coming back is electrolysis. I actually have an appointment booked for my back and diaper zone next week. I've had minor electrolysis appointments in the past, touch ups mostly, while it's a pricey service it's not nearly as painful as waxing appears to be and with a follow-up treatment the follicles are more a less all closed up, you can expect some hair to grow back, but it's barely noticeable like peach fuzz.