When I am working in the Capitol Hill area I stay in an Area 14 lodge called Pamlili Lodge. It's MK 7,500 or about $26 per night, very clean, quiet, large rooms and very good service. They did my laundry for free and cooked for me. The only downside is that it's not near very much except a small shop, hair salon and Nigerian restaurant, but for everything else you'll need to take a cab.
Phone: +265 999 151 676 or 01 978 560.
I tried to add to Tripadvisor accommodation list but they wouldn't let me.