The Ingalls family, as depicted in the Little House book series, were Christian, but the specific denomination is never mentioned in the books. The family is shown attending church services and praying, but the text does not indicate what denomination of Christianity they followed.
It is well known that Laura Ingalls Wilder was raised in a Christian family and had a strong faith in God, which is reflected in her books. There are many mentions of the Ingalls attending church, praying, singing hymns and reading the bible. However, her faith is not explicitly linked to any specific denomination, the religious aspect of the series is rather treated as a part of the daily life and culture of the Ingalls family and the society they lived in.
This is not entirely unusual. Since most frontier towns only had one church, that was the church that the Ingalls family attended in each town they lived in. In Walnut Grove, they attended the Congregational Church. In De Smet, SD, Charles Ingalls helped found and build the First Congregational Church which held its first service on August 30, 1882.
For more on Laura’s faith, A Prairie Girl’s Faith: The Spiritual Legacy of Laura Ingalls Wilder by Stephen W. Hines is an in-depth look at Laura’s spirituality.