Does your YouTube channel have an RSS feed? That might work if your site has a way of easily placing an RSS feed of your videos. My blog theme has a way of easily sticking any RSS feed in the blog sidebar. So you might want to consider something similar if your site has a way of doing it.
Short of that, I'm not sure what to tell you. You can easily embed any YouTube video by hand, but that doesn't sound like what you are looking to do.