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Kilimanjaro Review offers a number of suggestions on where to pick up gear, and several have Sunday hours:
Ezzy Spot Gents' Quality Garments
AS Osman Outfitters
The biggest and best shopping mall is the TFA Centre, often referred to as the Shoprite Centre, where several safari outfitters are located. It is open Mon - Sat 0900 - 1900, Sun 0900 β 1600.
Gear rental is also an option, and some make arrangements in advance of your arrival:
Ascend Tanzania
Base Camp Tanazania
Climbing Kilimanjaro
African Environments