Yes, coins were issued in the name of Southern Rhodesia (Zimbabwe), but circulated in Northern Rhodesia (Zambia) and Nyasaland (Malawi) too. Well, it was just 23 years (1932-1955).
Krause indicates that Northern Rhodesia was controlled by the British South Africa Company from about 1895 until 1923, when it was annexed by the British government. It does not list any specific coinage for the area during that period--they could have used South African coinage, or East Africa coinage during that period.
(Northern Rhodesia shared a border with what is now Tanganyika, which would have been part of (British) East Africa after World War I, and would have been German East Africa prior to World War I.)
Quote: "halfdisme"they could have used South African coinage, or East Africa coinage during that period.
The Southern Rhodesian and South African pounds were at par with the British pound (or "home currency" as it is often referred to), so it's probably not out of the realm of possibility that in say, 1928, some mixture of the SA and British pound coins circulated in Northern Rhodesia before SR pound coins were first minted.
I don't think East African coinage sounds too likely, though; given that like you say, until 1919, British East Africa was separated from Northern Rhodesia by GEA, and it was denominated differently. Would've made more sense for home currency and the SA pound to be in circulation until coins and notes of the SR pound began production in the 1930s (well, the coins).
Coins did not circulate in the territory of current Zambia until traders of the British South Africa Company began to work in the area in 1889, establishing formal control (Protectorates) from 1911. Since Zambian soil is rich in copper and is next to Katanga in Congo, I believe that before coins were introduced, copper "Katanga crosses" of different size and form were uses as money in the area.
Like in other British colonies in Southern Africa, British coinage was first introduced by colonists in the territory. Then it was supplemented in 1923 by South African coins and since 1932 by Southern Rhodesian coins.
I collect coins and tokens which circulated in Africa from 18th century to 2000. I sell about 7000 illustrated world coins from http://www.avscoins.com.
Well, they weren't an independent country per se, but a British colonial entity (protectorate until R&N was formed in 1953, if I'm not mistaken) in various forms until 1964.
Many colonies didn't have their own coinage, and used "home currency"- coins as used in the "mother" country, such as French Madagascar for example (until their own CFA Franc issues started in 1948).