Holy Name Society, Confraternity of the Most Holy Rosary, Third Order of Penance of St. Dominic, Third Order of Penance of St. Francis, Third Order Carmelites, Benedictine Oblates... there are also some associations that were spread by the Jesuits of old, but most of these are in Latin countries.
For all of these lay associations or third orders, it is recommended to only use the pre-Vatican 2 books, i.e. constitutions, rules, etc.