Train’s song is a little ambiguous, the singer is addressing a woman he’s never actually spoken to. He certainly *wants to be *in love.
An upvote for Paintcharge’s suggestion of *This is Us *by Mark Knopfler and Emmylou Harris. The singers are a married couple reflecting positively on the history of their marriage.
One can’t really have a better example than the first one, although after listening to it I know why I’ve never heard it. 
Thanks Mr. Parker!
The impetus for the question is that recently I’ve been listening to a lot of pop music from the 20’s to the 50’s and there are a number of songs that talk about getting married. (Dean Martin’s “Ain’t that a kick in the head” might be the most amusing.) I don’t listen to a ton of today’s pop music (obviously) and didn’t know any similar songs. I thought it might be a sign of the times more than my ignorance, but perhaps not!
Where are all the pop songs that some people play at their weddings?
Cake by the Ocean by DNCE - 2016
wedding cake of course
Does Meghan Trainor’s “Dear Future Husband” count? It’s not about wanting to marry a specific guy but it is about marriage and how this woman expects to be treated by the man she marries. It got to #14 on the US charts in 2015.
But marriage is still portrayed in a positive light in the lyrics, which is what I think the OP is going for, no? I mean, “Wouldn’t It Be Nice” is also written from a singular POV, too.
Certainly not the last pop song, but Paul Stookey wrote The Wedding Song and performed it for Peter Yarrow’s wedding back in 1969. The song is still a favorite at weddings and is performed constantly. I performed it at a wedding not too long ago, as a matter of fact.
Meh, no biggie.
Don’t think he’s talking about wedding cake.
Brad Paisley, by all accounts very happily married, has had several country hits mentioning marriage in a positive way:
“She’s Everything” (#35 on Billboard)
Brad Paisley - She's Everything Lyrics | AZLyrics.com“Waitin’ on a Woman” (#44 on Billboard)
Google Play Music is no longer available“Letter to Me” (#40 on Billboard)
Brad Paisley - Letter To Me Lyrics | AZLyrics.comThat was going to be my suggestion: https://www.youtube.com/watch?v=PIh2xe4jnpk
Taylor Swift, “Love Story”
Taylor Swift - Love Story Lyrics | AZLyrics.comI see your point, but I think I’m going to stand by my opinion. At least the singer in “Wouldn’t It Be Nice” is looking forward to spending the night and kissing. It sounds like he singing to his high school sweetheart. The singer in "Marry me"speaks generically of wearing white at the wedding, but not much about their future together. He’s singing to a woman he hasn’t said hello to yet.
Perhaps I’ve just listed to too many of my male friend’s sighs of love over waitresses or long ago school-mates they never actually spoke to.
How about In Spite of Ourselves, by John Prine (with Iris DeMent)?
OK. I just took the OP as perhaps hinting that marriage is no longer an institution in pop culture that is represented as something to aspire to. Fake lover you never talked to or not, the song portrays marriage as a relationship goal for the singer, when he can simply sing about sexy time, if he wanted to.
I don’t know if this made it in America, but: Magic! - “Rude”
(He wants to get married - SHE wants to get married - it’s Dad that’s kicking up). From 2014
ETA : and I could have sworn I read the thread properly! :smack: