<p>I've been trying to convert SVG images to PNG using C#, without having to write too much code. Can anyone recommend a library or example code for doing this?</p>

You can call the command-line version of inkscape to do this:
http://harriyott.com/2008/05/converting-svg-images-to-png-in-c.aspx
Also there is a C# SVG rendering engine, primarily designed to allow SVG files to be used on the web on codeplex that might suit your needs if that is your problem:
Original Project
http://www.codeplex.com/svg
Fork with fixes and more activity:
(added 7/2013)
https://github.com/vvvv/SVG