We don't support URLs such as yourdomain.com/blog, but we can set up a subdomain for you, such as blog.yourdomain.com.
All we need in order to do this for you is the A Record or CNAME Record from your blog host, your tumblr account, or whatever else you'd like to put at this subdomain. You can contact support@otherpeoplespixels.com to set this up.