I am using Visual Studio 2010 and using web deployment to promote the .Net MVC site to specific environments. I installed Elmah, and it worked great on my DEV environment, but
I know that is an old question, but I have a similar problem and landed here, so perhaps my answer is still helpful for others.
Simply add this to your project file of your web application in a prefered PropertyGroup-element:
bin\System.Data.SQLite.dll