There's always "On the Street where You Live," although it's high for a baritone. Two from Fiddler on the Roof would be "Do You Love Me" and the song Motl sings to Tzeitl that ends, "God has given you to me." "Sixteen going on 17" from The Sound of Music is very sweet, but it's a bit creepy given that Rolf goes on to become a Nazi. Speaking of Nazis, "If You Could See Her from My Eyes," from Cabaret, is also a creepy love song.
My all-time favorite, which works very well for a baritone, is "Music of the Night," although that's more a seduction song than a love song. I've heard "All I Ask of You" done as a wedding song (if you have a second singer), but I definitely prefer MOTN. If you're looking for a bit of ironic humor, how about "I've Grown Accustomed to Her Face"? For Higgins, that's as close as he'll ever come to a love song -- something like Mr. Spock singing to his soulmate.
Audrey, the Phantom Phanatic, who nonetheless would rather be Jean Valjean, who knew how to make lemonade out of lemons.