Rhodesia did have Black Members of Parliament (MPs), though the nature of their representation and how they were elected changed significantly as the political landscape shifted from the 1961 Constitution to the "Internal Settlement" of 1979.

1. The 1961 Constitution (The First Black MPs)
Under the 1961 Constitution, the franchise was split into the "A" and "B" rolls. This system guaranteed that at least 15 seats in the 65-seat Legislative Assembly would be elected primarily by "B" roll voters (the majority of whom were Black).

The 1962 and 1965 Elections: Several Black candidates were elected, mostly representing the United Federal Party (UFP) or running as independents.

Notable Names: Figures like Josiah Gondo (who became the first Black Leader of the Opposition in 1965) and Chad Chipunza served during this era.

The Boycott: Because mainstream nationalist parties like ZAPU and ZANU boycotted these elections, the Black MPs were often viewed by nationalists as "collaborators" or "sell-outs" rather than true representatives of the people.

2. The 1969 Republican Constitution

After Ian Smith’s government declared Rhodesia a republic, a new constitution was introduced that formalized racial representation. It created a 66-seat House of Assembly:
50 seats were reserved for whites.
16 seats were reserved for Blacks.
8 were directly elected by Black voters.
8 were "indirectly" elected by colleges of Tribal Chiefs and headmen (who were seen as more sympathetic to the government).

The Senate: A Senate was also created, which included 10 Black Chiefs alongside 10 white Senators and 3 appointed by the President.

Things changed massively however in 1979, because by that time Rhodesia become "Zimbabwe-Rhodesia" for a short while before becoming Zimbabwe.