Interior door handle with privacy lock for 2-inch think interior doors
So, this is a little out-of-line, as shopping advice goes stale fast out there in the world, but do this:

go to build.com and search &quot;interior privacy lockset 2&quot; door&quot;
in the side column, headed &quot;Narrow Your Results&quot;, under 'function', select privacy.
same column, under 'door thickness', select 2&quot;
sort low to high price and you'll find an array of decent options