The cleanest way to do this that I have found is to modify the proect file (.csproj) directly in a text editor.
If you have a project that already has the desired configuration, open it up and find the appropriate PropertyGroup element (e.g. the one for the "Demo" configuration below).
Copy that PropertyGroup element and paste it after the equivalent element for the Debug configuaration.
If you do not already have one with the desired configuration for some reason, you should just be able to copy the Debug one (or Release if it is more appropriate) and change the name from "Debug" to whatever your configuration name is.
<PropertyGroup Condition="'$(Configuration)|$(Platform)' == 'Demo|AnyCPU'">
<OutputPath>bin\</OutputPath>
<DefineConstants>TRACE</DefineConstants>
<DebugType>pdbonly</DebugType>
<Optimize>true</Optimize>
<PlatformTarget>AnyCPU</PlatformTarget>
<ErrorReport>prompt</ErrorReport>
<WarningLevel>4</WarningLevel>
<CodeAnalysisRuleSet>MinimumRecommendedRules.ruleset</CodeAnalysisRuleSet>
<Prefer32Bit>false</Prefer32Bit>
</PropertyGroup>