The New York Times had a lovely article about how some couples prefer private vows. If you have a subscription, you can read it here:
Here are a few ways my couples have chosen to say private vows:
Sometimes, they want to say their vows during the ceremony, but just to each other. If they’d like to do that, I’ll say, “Justin and Susan have chosen to make their vows just to each other.” That way, people aren’t upset because they can’t hear; they accept that the vows are private.
Many couples do want to say something out loud after their private vows. They may do this as they exchange rings, saying something like “This ring symbolizes what my heart already knows, that we choose each other to live our lives together.” Or they may say a more generic vow, like “I take you for my partner, my love, and my co-mischief maker forever.”
Some couples choose to make vows to each other outside of the ceremony, usually just before. In that case, I might say, “Allison and Kaylie have made their vows to each other today” and continue with a ring exchange or generic vow.
In every case, the ceremony acknowledges that a covenant has been made and accepted between the two. In every case, it’s lovely.