Marriage not Dating, 
Oops you already watched it...Try.. Easy Fortune Happy Life, Its an older T drama
I answered to a similar question here, so that may help you.

However, none of the following three have female leads that are forced to stay with the male leads because they're poor. It's more because the male lead is in love/attracted and makes her stay with him against her will, often by threatening her relatives/friends because he's powerful and wealthy.

- Lady & Liar has rich guy/poor girl theme AND forced marriage (well technically, engagement) BUT memory loss! It's not so bad because the story actually centers around that, so it's not random last minute amnesia 
- Sealed With a Kiss has rich guy/poor girl theme, and the male lead forces the female lead to stay with him, but without marrying her
- Cruel Romance has rich guy/poor girl theme, and he falls in love very soon and is very forceful, but he doesn't force her to marry him 
http://mydramalist.com/371-that-fool

Don't know if you want to watch Thai dramas (lakorns), but this is a pretty common trope in them. I'd recommend Roy Marn, Manee Yard Fah to begin with.
Thai Full House. Amazing, truly.
Autumns Concerto isn't quite the same thing, but it has similar themes, you'll like it!
I LOVE CONTRACT MARRIAGES/FORCED TO BE TOGETHER DRAMAS!!!

Have you watched 1% of Anything? The original version was aired in 2003, starring Kang Dong Won (one of his TWO dramas he ever acted in). The remake is currently airing, starring Ha Suk Jin! It is about a guy who is required to marry a lady to get his inheritance so they had a contract to date for 10 months. The guy is a chaebol and the lady is not very rich. Fits your description perfectly!

9 Ends 2 Outs is amazing as well. It is less of contracted marriage... but they were best friends and they were 'cohabiting'. In my very very very honest opinion, I think it is better than In Time With You (the Taiwan version) even though the cinematography might not be as good because this drama depicted the dilemmas of best friends turned lovers very well.

It's Okay, Daddy's Love has a part about contracted marriage as well but they aren't the main lead... the guy is a chaebol and the lady is forced to marry him because her dad ran into some trouble and they ended up owing lots of money.

Dandelion Family (aka Blossoms Sisters) has a side couple with contracted marriage as well. I was fast forwarding the whole drama to only their parts but I have yet to finish. I plan to watch every single episode when my semester ends.

Drunken to Love You (Taiwan Drama) which was written by the same scriptwriter who wrote Fated to Love You. I did not watch the drama but I know it's about contracted marriage as well because I could not feel the chemistry between the main couple (it's just me because my OTP ended up as the second male lead loving the main female lead).
High Society has both a rich male + poor female and a rich female + poor male couple. The families of the rich characters also seem to push towards marriage a lot (setting up dates etc).

edit: oh.. i just saw this thread was from a year ago so i doubt this is still an ongoing search haha. oh well it might help anyone looking for similar stuff :)
I agree with Ari, Mary Stayed out all Night fits all of your criteria
If you're still looking, I have some dramas here with a similar concept, we have:
¤ Twenty Again - Forced marriage from a young age but the drama doesn't focus on that unfortunately, it's more about that the marriage ruined the female's life and she's trying to make up for it by studying again and living her life.
¤ From Five to Nine - (japanese drama) not really forced marriage but it's more like one party wants to marry the other who doesn't want to..
¤ Innocent man - Here too, doesn't focus on the concept but it contains it
¤ Please Come Back, Mister - Same here, doesn't focus on it but some parts are about it
¤ Nigeru wa Haji da ga Yaku ni Tatsu - (japanese drama) This one is more about Marriage de Facto, like a contract marriage, pretty interesting

Then for the Rich guy and Poor woman:
¤ Rich Man, Poor Woman - literally, the title says all about it xD
¤ Cheese in the Trap
¤ City Hunter
¤ Cunning Single Lady
¤ Flower Boy Next Door 
¤ High Society - this drama has both, poor girl rich dude and poor dude and rich girl
¤ Jealousy Incarnate
¤ Love Me if You Dare
¤ Oh My Ghost
¤ Secret
¤ The Heirs
¤ The Master's Sun

I hope you'll like them
I also recommend Thai Full house, even do it wasn't a forced marriage but they did have to get married.
Marriage Contract
my woman.. it was so awful i couldnt stand it.. it was like getting punched in the stomach..   It wasnt a bad drama, but you have to watch it to see what i mean.