Have you tried just giving him blank paper and see if he prefers coloring his own pictures?
Scribbling is actually an important pre-writing skill, but there are a lot of different things that could be making this activity less desirable for him.
It might be that he is intimidated by the idea of having to color inside lines. In which case, offering him blank paper will make all the difference.
He may also have some strength/grip issues. You can try other types of writing materials that do not require pressing as hard. colored chalks and oil pastel crayons are a little messier, but don't require quite as much force for application. If you find he needs better strength. Play dough is the answer! the more he plays with and kneads dough, the stronger his little hands will get - and it is fun.
It may be an issue where he is asserting independence. He is pushing boundaries and buttons because he is about four and it is his job to do so. If he is feeling forced, he may have an issue with being told he absolutely must sit and color right now. At this age, a really great way to give him a sense of control and independence, without losing your ability to guide him where he needs to go is to offer choice. "Would you like to color Pooh Bear today, or make your own picture?" This way, he knows it is coloring time, but he still has a sense of control over how he uses that coloring time. He should also be allowed to decide when he done. Even four year olds deserve a little respect and control over their own activities to some degree.
It is also possible your son has a sensory problem with the feel of paper or the sound of writing. If he likes to write/draw under other circumstances, this is not an issue. If he does not ever want to write at all, you might eventually look into sensory issues. Give it a little time first, try some of the other suggestions and see if he just grows out of it in six months or so. If not, look into possible sensory challenges. There are actually a lot of ways to help with sensory issues as well, but he may need professional intervention for a little while if this is the case.