There is a custom known as a Josephite marriage (named in honor of St. Joseph’s marriage to the Blessed Mother), in which the couple agrees to permanently live without marital relations. Any couple contemplating such a route should speak with a balanced, trusted, and orthodox spiritual director or confessor before attempting it; such a marriage is very rare and should not be entered into without just cause and proper pastoral guidance. One couple who thought such a marriage was for them were Louis and Zelie Martin, a nineteenth-century French couple who decided to live as brother and sister after they wed. When their spiritual director found out, he told them that they were not called to a celibate marriage. Good thing, too. Louis and Zelie Martin subsequently had five daughters who entered the convent, the youngest of whom became known as St. Therese of Lisieux.
As for a St. Joseph’s Night, a custom by which the couple puts off marital relations the first night after their wedding, I have never heard of it and I could find nothing about it on the Internet. You might ask a research librarian at a city or university library to help you see if more information is available. If such a custom existed, it was most likely a pious devotion and not incumbent upon newlywed couples to observe.