The green paint on the wall provides a suitable contrast with or to the yellow doors.
If I use with will that make this sentence wrong?
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The intention/goal of the sentence is to emphasize the contrast between the green paint on the wall and the yellow doors. The correct idioms for such a goal may be in contrast with or in contrast to. Neither is incorrect.
However, your sentence will have to be rewritten thus to make it grammatically correct:
The green paint on the wall provides a suitable contrast to the yellow doors.
The green paint on the wall is suitably contrasted with the yellow doors.