The only semibudget option in Mana Pools are these well-equipped lodges and campsites along the Zambezi River at Nyamepi, which offer prime animal viewing. Campsites are inclusive for six people, so it's not great value unless you're in a group (otherwise you can pay per-person rates on arrival).
Lodges have two bedrooms, a fully equipped kitchen and bedding, but they book out during July to October, so you'll need to make reservations well in advance (accepted one year ahead).
You'll need to book through the Harare office by phone or email. They also have some more remote bush camp sites.