“You Matter To Me” from Waitress. Very new (therefore original), is perfect for piano and cello, and just so meaningful. Try the concept album version.
Although this isn't from a show, it has been recorded by Barbra Streisand, though I prefer the performance by Kevin Dozier, "On My Way To You," especially if the two getting married aren't kids. Here's a video of Kevin singing it (he actually has more views that Babs) https://www.youtube.com/watch?v=fcKeWVPBtMY
it's written by the Bergmans and Michel Legrand, so it has theater cred. It's NOT easy to sing -- you need real pipes to do it well. It's on Kevin's album "Love-Wise" with a gorgeous arrangement by Christopher Marlowe.
I just checked and Kevin's studio recording is at iTunes -- the arrangement has oboe and cello and piano -- it's really gorgeous -- though you'll see that with just piano it works fine -- as long as you have a first rate singer. Good luck!