Alright @inplainsight, I see your challenge, and here goes my response. I don't know how well it would work for other people, but these songs have served me well.
Now the thing is, these songs mightn't work for everyone because they aren't really about courting a potential partner. These are some of the songs that have been staples in my relationship with my girlfriend of 5 years. They are songs that matter to one or both of us for different reasons. Realistically this list could be much longer, but I'll try to pick the best 5.
Hobey ho, let's go.
Crush'd - Say Anything
This song is perfect because it's the appropriate level of serious and jokey. Really good at the outset of a mixtape, but also very clear in it's intention. You have a crush on this person. It's sweet and sentimental and has a weird line about Oedipal things.
Cheerleader (Acoustic) - Omi
As soon as my lady showed me this song I was hooked. I think it's just so happy and beautiful, a little funny and very dancy. She insisted that I put this song on the list >.<. However, I think if you want it to fit in better with the rest of the songs on this mixtape, then you're gonna have to go with the acoustic version. It's got a little more soul in it, but still is true to the studio version.
The Missing Piece - Forgive Durden
This song comes out of a pop-punk style rock opera/musical called Razia's Shadow. It's actually a great album if you ever have the time. In any case, though, this is a romantic, soft, kind of upbeat song. It's low pressure and it's got both male and female parts. It also has one of my favorite lines of the album - "Place your hand on mine, untie your mind" (which is actually in three songs but best in this one.)
Your Guardian Angel - Red Jumpsuit Apparatus
This is such a somber, solemn song, and a throwback to both of our early high school days (we didn't know each other then). The older I get, the more I feel like it's a little over dramatic, but it will always be special to us.
The Book of Love - Peter Gabriel
I don't think any other song so perfectly encapsulates love to me, or in my relationship. Every time I hear this song it makes me think of her, and when we listen to it together... well, there just aren't words to describe it. If you know, you know. Listen to this song with the partner you're looking into or have.