I recently found out about a external render engine called Kerkythea.
When I download it, it gives me a blender application.
When I open the blender application it brings me to blender 2.48.
So I open a project I was working on in the blender 2.48 application.
And it loads up fine.
When I switch it to render with Kerkythea and hit render it just shows a black screen in the render box.
The same thing happens with Yafray.
I have a Intel Mac OS X. With 1 GB of RAM and running Snow Leopard.
I m not sure if i understood but i think you downloaded the Blender2Kerkythea application.This does indeed give you a black screen.It only export your Blender scene to a Kerkythea scene( an .xml file i think).You have to open that file using the real Kerkythea app whci you 'll find it http://www.kerkythea.net/joomla/index.php?option=com_remository&Itemid=42&func=select&id=2
Yep, I downloaded Blender2Kerkythea. Currently downloading the app. 
It just appears as a folder in my applications.
Yafray doesn’t exist anymore. It has evolved in Yafaray, it uses a Pyton script instead of being included in the render panel of Blender. Check the Yafaray website for more informations.
I have never used Kerkythea, but usually, external renders and Blender deal with lamps differently. So your black screen coud be a problem of light. E.g. area lamps: with Blender Internal, area lamps have a huge intensity, whereas in Yafaray or Luxrender, they produce a much dimmer light.
Read the general workflow notes:
http://www.yafaray.org/documentation/install#workflow
Use the examples if you get unexpected results:
http://www.yafaray.org/download/examples
It just quits when I try to even just render the default scene.
Are you using lighting that is compatible with yaf? Sound like you don’t have any light sources or an environment