One of the major annoyances with Sandboxed solutions is that you cannot deploy custom icons/images for any of the SharePoint Features that you develop. Even though you can easily add the “Images” mapped folder to your SharePoint Sandboxed Visual Studio solution and build/compile the solution, the deployment will ultimately fail.
Why is this?
This stems from the inherent limitation of Sandboxed solutions restricting a developer from being able to deploy things to the SharePoint file system, even such minor things as an Icon/Image file.
Though, there may be available workarounds available on the Internet for deploying a custom icon/image with your Sandboxed solution (the default icon is a SharePoint gear), the most conventional approach is to simply associate the ImageUrl with the SharePoint Feature and deploy the solution as a Farm solution instead.
Maybe in future versions of SharePoint, there will be a way to deploy Sandboxed solutions with custom icons/images, but for now, as horrible as it may sound, opt for the Farm Feature (if the custom icon/image is an absolute requirement) to get your solution up and running….