Eagles - Love will keep us Alive
James Taylor - You’ve got a Friend
Sammy Hagar - Kama (the lyrics are great, and you could just insert the name you need)
Of course there’s the wedding standards:
Sheriff - When I’m with You
Frozen Ghost - Dream Come True (my personal favorite at my wedding)
… which interesting enough are written by the same guy in who was in both bands.
Sorry, no links at work.
I recommend you turn to Broadway.
Take Me As I Am–Jekyll and Hyde
“Love meaning me,
Love meaning you,
We’ll make that one dream come true!
You know who I am…
Take me as I am.”
Damn, most of the ones I can think of are for sopranos but I’m going to keep thinking. How does the bride feel about country? There are a lot of love songs for altos in the country genre.
ooo ooo ooo how about The Rose by Bette Midler? That’s for an alto and it’s really pretty.
“Some say love, it is a river
That drowns the tender reed
Some say love, it is a razor
That leaves your soul to bleed
Some say love, it is a hunger
An endless aching need
I say love, it is a flower
And you, its only seed”
Time After Time for her
If you can find a clarinetist, try E lucevan le stelle for him. Perfect guy song for marriage 
She has come up with two suggestions…You’ll Never Walk Alone and You Light Up My Life. Neither of which I can sing with a straight face. But they were sung at her mom’s wedding, so she thinks it might be nice.
Kill me now.
My number 1 pick: Real Love - John Lennon (Listen to the Regina Spektor version to hear a woman sing it)
Here There and Everywhere - The Beatles
Two Of Us - The Beatles
If you’re not the one - Daniel Bedingfield
I’m Yours - Jason Mraz
Perfect Day - Lou Reed
Ben E King’s Stand By Me. Beautiful sentiment and if you get a backing with the bounce of the original it really gets people happy.
When the night has come, and the land is dark
And the moon is the only light we will see
No, I won’t be afraid, oh, I won’t be afraid
Just as long as you stand, stand by me
So darlin’, darlin’ stand by me
Oh stand by me
Oh stand, stand by me, stand by me
“Not While I’m Around” - from Sondheim’s Sweeney Todd
“Enjoy the Silence” - Depeche Mode
“'Til There Was You” - from Willson’s The Music Man
“Hands To Heaven” - Breathe
“(I Just) Died In Your Arms Tonight” - Cutting Crew
and of course
“In Your Eyes” - Peter Gabriel
No, the eighties never did end for me.
Simon & Garfunkel - Song For The Asking
This is why people shouldn’t be allowed to plan their own weddings. Were I at a wedding where either of those songs were featured, I can guarantee you I’d be laughing into my sleeve the whole time. How can those not sound like karaoke?
Oooh, forgot one…cool, modern, sweet.
That’s what I like about you-Trisha Yearwood
What I like about you-The Romantics
Keep your hands to yourself-Georgia Satellites
Right down the line-Gerry Rafferty
Jason Mraz is a good choice, depending on the circumstances, but I wouldn’t suggest I’m Yours. It strikes me as kinda frivolous. Plus, the lyrics don’t really reward close scrutiny (it’s your godforsaken right to be loved? What the hell does that mean?).
I’d suggest the next track on the same album (We Sing, We Dance, We Steal Things), Lucky. It’s a very sweet love song that he sings as a duet with Colbie Caillat. Only catch is that the OP would need to find a gentleman to sing it with her.
I’ve always found it the height of injustice that no one ever sings Aqualung at weddings. Maybe you could rectify that. 
Or, more seriously, Dan Fogelberg’s Longer never goes out of style. Another one that would benefit from a second singer, though.
How about Ann Murray’s You Needed Me? If either one of them happens to be a massage therapist, it could even have a hidden meaning.
OOh, I love “Til There was You…”
Just an update, as I was searching threads for music suggestions for my daughter’s wedding in three day and found I’d never come back to this thread…
The minister (groom’s uncle) was very adamant that no “secular” songs be sung, so he approved You’ll Never Walk Alone…which is a song originally sung to a pregnant woman whose husband has died and doesn’t mention God or religion at all… so I found an arrangement, dropped the key way down (my poor pianist!), and sang it, altering the one high note I just couldn’t hit that day. The bride’s grandmother gave me such a hug afters. That song was sung at her wedding, and my good friend sang it at their 25th anniversary party. I snuck one peek at my friend and at the bride while I was singing, and almost started crying, so I went back to singing to the hook on the wall.
Oh, and I discovered that song is used as the theme song for the Liverpool Soccer Club. Made it a little more palatable to sing!
My suggestions are “My Only Love” by the Statler Brothers and “One Hand, One Heart” from West Side Story.
Did you ever break it to the minister that it was, in fact, a secular song?
Anthony Hamilton’s Dear Life.
He’ll Make Me Happy from The Muppets Take Manhattan. I wanted to walk down the aisle to that, but since it was a Roman Catholic mass, it wasn’t allowed… boo.
You could get a second person and sing “When God Made You”, or use a backing track for the harmony.