My question is
If a hindu married couple want to remain child free in their whole life though they able to produce children is it a sin in Hinduism for a married woman not having a children, though she is able to give birth of a child. Please answer me
Yes, a Hindu married couple can remain child free or not give birth to any children and there is nothing in the Hindu scriptures against it.
First, you need to understand some basic concepts. The Hindu scriptures are the Vedas—The Rig Veda, Yajur Veda, Sama Veda, and Atharva Veda. These are the only eternal scriptures of Hinduism. However, the Bhagavadgita is also considered a scripture but if there is a conflict between the Bhagavadgita and the Vedas, the Vedas should be given priority.
From time to time, various social codes were written like Manu Samhita, which had rules for the social and individual conduct of a person. Today all these codes are irrelevant as we have other codes of the society like the Indian Penal Code.
So, if you do not want to have children, there is no problem in Hinduism with that. However, if you can direct your attention towards spiritual life and knowing your self and realizing God, then that will be an added advantage.
With best wishes,