This is fairly simple to accomplish with an MSBUILD file.
Here's a sample target the will rebuild your entire solution and will deploy your MVC web application to your desired output directory
<Target Name="Deploy">
<MSBuild Projects="Solution.sln" Targets="Rebuild" />
<MSBuild Projects="MVCWebProject\MVCWeb.csproj"
Targets="ResolveReferences;_CopyWebApplication"
Properties="OutDir=$(OutputFolder)\bin\;WebProjectOutputDir=$(OutputFolder)" />
</Target>
In your cc.net configuration, simply pass /p option to the MSBUILD task to specify the output directory for your web application as follows:
/p:OutputFolder=c:\Your\Output\Path