There is no private permanent accommodation on Mount Kilimanjaro, on any of the routes. This keeps the mountain as pristine and undeveloped as possible, for the benefit of everyone.
The good news, however, is that sleeping tents are usually only shared between two climbers, and you can also upgrade your climb to have a tent just for yourself. Seen that way, all accommodation on Mount Kilimanjaro, with the exception of the Marangu Huts, may be considered private!
For maximum privacy, climb on a quieter route, such as the Northern Circuit. That way, you can also avoid sharing your campsite with the crowds.
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