My first inclination is that it should be relatively easy to promote just about any type of coupon site, especially in the current economy. I don't know what kind of budget you are working with, in terms of marketing, but things can be done relatively inexpensively.

A couple of ideas that I would start with would be creating ads to be posted on Craigslist. You could also do a very simple YouTube video introducing the site. It doesn't even need to have actors - it could just provide several slides that explain some of the key points about how the site works, etc. The video would of course link to the your freelance writing site. You could also create an "Research Paper and Essay Writing" channel on YouTube that hosts videos/presentations that provide various writing tips and/or success stories from your site users and/or clients.

You could also advertise an affiliate opportunity for the placement of banner ads. I am not sure if the affiliate program will work right now though, since your site is currently totally free to everyone (as I assume at least, after having reviewed sites similar to EssayCoupons.com)....I am not sure how you plan to produce a revenue stream for the site that would in tern allow you to compensate affiliates. Anyway, those are some of the ideas of how I would promote your essay writing site, with YouTube being the priority, followed by Craigslist in second place.