Is there any legitimate reason for coercion in a democratic society?
This depends to some degree on what you mean by “coercion.” If coercion is simply defined as government forcing people to do things that they do not want to do, then there is absolutely a legitimate reason for coercion in a democratic society.
Even in a democratic society, not everyone will want to obey the rules that have been set out democratically by elected officials. When people are not willing to obey rules, coercion must be deployed if the government is to retain its credibility and legitimacy. Let us imagine, for example, what would happen if the government did not coerce people who failed to pay their taxes. If the government refrained from punishing such people, no one would pay their taxes. If no one paid their taxes, the government would fall apart and our society would fall apart with it.
It is not legitimate for democratic governments to try to do things like coercing belief or opinion. The government has no legitimate reason to try to force people to believe, in anything, even in democracy. However, there is certainly a legitimate reason for coercion to compel people to follow the rules of the society.