"Sub rosa" (from medieval association of the rose and secrecy; from 1654) - the deals are done sub rosa.
Dictionary: sub rosa

Alternatively, if this is simply someone choosing to deal with friends, acquaintances or references, I think "privately" is fine - they are allocated/contracted privately. If the purpose is avoiding taxes and fees, the deal is "shady", or something about it is illegal, and therefore everything needs to be kept quiet, then "under the table" is my suggestion - the deals are done "under the table" rather than in the open market.

are mostly disposed of privately and do not come onto the open market

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perfect! Thank You!!