I think you need to expand a little on what you are asking.
People can be blessed by priests and deacons for many occasions and reasons. While I was engaged to my husband, a deacon imparted a blessing on us after mass one Sunday-- blessing us and asking God to help us grow in holiness as we prepared for marriage. I believe there might be a blessing for engaged couples in the Book of Blessings.
That isn’t the same thing as “blessing” an unmarried couple relationship that is contrary to the faith (i.e. cohabitation). What exactly are you looking for from a blessing and what type of relationship is being blessed?