'private needs' is correct and usable in written English.
You can use it when referring to something that one wants or requires for their own personal use. For example: "The company operated outside of its employees' private needs."
This is impractical, though, for most business and private needs.
Anglican leaders speak of a society awash with "pick and mix" spirituality, in which people choose beliefs and practices to suit their private needs.
During the 70's, Mr. Sikkema learned to balance public policy and private needs as a commissioner of public housing in Amsterdam.
It calls for an activist government on the alert for public palliatives for private needs, at least the needs of swing voters.
Sophie devoted her life to the private needs of a public man in his waning years, who, according to Todd, suffered from depression and alcoholism, and was dependent on amphetamines and sleeping pills.
There is something beyond mere Pop parody or social provocation in the work, something to do with deep private needs and desires, which we perceive secondhand as comic pathos.
For her, emotional expression does not well up from a private need for personal honesty.
The private need beneath the public display is what the work, with intermittent success, seeks to expose.
It dawns on us also that our own reliable family memories are probably being reshaped, day by day, to meet some private need.
He repeated his call for statisticians to be more agile when thinking about the statistics that users in the public and private need.
But here Kreon makes a plausible political case, one the Greeks would certainly have understood, in arguing that loyalty to the city takes precedence over private need.
