First sentence:The man is poor and contented. has no error.
poor is an adjective to the noun man
and is a conjunction
contented is adjective to the noun man (similar to content)
There is no syntactic error as both poor and contented are adjective qualities for the man in the sentence.
The second sentence : The man is poor contented is syntactically correct as the poor is a quality of the adjective contented to negate it to mean 'not much' contented.