I’m looking to make a CD of love songs that aren’t all that lovely. I’m looking for songs where the singer is not getting the girl but is desperately in love with her. I would like them to have nice sound as well, it has to be mellow, something like Playground Love in terms of sound. So far the only song I have that fits pretty well is Beautiful by James Blunt.
End of the Road-- BoysIIMen, although it verges on the pathetic.
Ain’t That a Shame-- Fats Domino
Dock of the Bay-- Otis Redding
Have You Seen Her?-- Chi-Lites
Whoa, why can’t I think of one single song in another genre?
I’m not sure if this quite qualifies for your description, but “And So It Goes” by Billy Joel is the best sad love song I know of. Gives me the chills.
Also maybe “Lately” by Stevie Wonder?
“Don’t Speak” - No Doubt
Bush’s Letting the Cables Sleep came to my mind second after Danceswithcats’ suggestion.
Me, too. That’s what I came in here to say.
I haven’t heard the songs listed in the OP, so I have no idea what mood you’re reaching for. That, of course, leaves me unconstrained by your wishes. 
These are some of my favorite sad love songs.
I’m listening to Chet Baker right now; all of his songs are, to me, sad love songs. Even when he sings about getting the girl, there’s a distance in his voice that’s melancholy. “I Fall In Love Too Easily,” maybe. It’s the mood it sets, I think, that fits your category.
If you like country, there are tons of great songs that fit what you’re looking for. “Please Remember Me,” by Tim McGraw is about a man who recognizes that she’ll move on without him, and be quite happy without him. “You Don’t Love Me Anymore,” another Tim McGraw song. Breaks my heart every time. The Dixie Chicks’ “A Home,” about what happens when you listen to all the people who tell you why your relationship won’t work. Lyle Lovett’s “She’s Already Made Up Her Mind,” where he tries to talk her into staying but, of course, she’s already made up her mind. 
Romeo and Juliet by Dire Straights
Mary Margaret O’Hara:
*
Not Having You, But Keeping You in Mind
You Will Be Loved Again*
“Annie Waits” by Ben Folds.
“Annie waits…but not for me.”
“Jessie’s Girl” by Rick Springfield.
Is She Really Going Out with Him? – Joe Jackson
Cry Me a River. I’m partial to Caetano Veloso’s version (which happens to be on the mix CD I’m listening to at this moment).
I Will Wait For You, by Connie Francis
The Shadow of Your Smile - any of Frank Sinatra’s renditions are good
Angel Eyes - again, Frank Sinatra
I’ll Be Seeing You - of the sixteen I’ve heard, I like Jo Stafford’s the most
All…oldish. But very nice, very mellow songs.
The saddest love song I know is I Can’t Make It Alone, by Dusty Springfield, from the incredible recording Dusty in Memphis.
I dare you not to choke up when she sings ‘Oh baby, I’m begging you…’
Beautiful Sadness, by Jane Olivor.
“Just because it’s over, doesn’t mean it didn’t happen…
doesn’t mean it wasn’t beautiful, even with the pain…”
"Same Old Lang Syne" by Dan Fogelberg. Oy, I’m getting verklempt just thinking about it.
“I Will Always Love you” - Dolly Parton
“You’ll Think of Me” - Keith Urban
“Love Has No Pride” - Linda Ronstadt
I second Dolly’s “I will Always Love You” – it amazes me that people sing it at weddings, apparently not listening to the words.
“Long, Long Time” by Linda Ronstadt is another.
“For No One” by the Beatles (McCartney wrote and sang it alone).
Early country music has some masterpieces of this kind. Two of my favorites are by the Carter Family:
“I’ll Be All Smiles Tonight” starts out with a girl singing about how she’s going to dress up for a dance that night. Subsequent verses reveal that the guy who dumped her will be there with his new bride, and that she’s determined not to let her feelings show. “Though my heart may break tomorrow, I’ll be all smiles tonight”. I always found it more powerful because the listener is the only one she’s sharing this with.
“I’m Thinking Tonight of My Blue Eyes” contains the incredible lyrics:
When the cold, cold grave shall enclose me
Will you come dear, and shed just one tear
And say to the strangers around you
A poor heart you have broken lies here
B.J. Thomas–Someone Done Somebody Wrong Song
The Tennesee Waltz, sung by about a million people
“Comfortable” by John Mayer.
“My Lover’s Gone” by Dido.
“Without You”, You Were Mine" and “Once You’ve Loved Somebody” by the Dixie Chicks.
“Helplessly Hoping” by CSNY.
“Can’t Let Go” Lucinda Williams.
“Wedding Bells” Lucinda Williams and John Prine…that one gets me every time.
“Who’s Lovin’ You” by Terence Trent d’Arby.