Can parties who enter into a regular marriage change or convert that marriage into a covenant marriage?

Parties can do so in the state of Arizona, which provides that parties to an existing marriage simply must sign and file the statement of covenant marriage, which reads:

We solemnly declare that marriage is a covenant between a man and a woman who agree to live together as husband and wife for as long as they both live. We have chosen each other carefully and have received premarital counseling on the nature, purposes and responsibilities of marriage. We understand that a covenant marriage is for life. If we experience marital difficulties, we commit ourselves to take all reasonable efforts to preserve our marriage, including marital counseling.