Can Lion OSX Search in App's Contents
Easy Solution
For a free GUI solution, you could use EasyFind. To search inside applications, you just need to check "Package Contents" in the sidebar.

For a quicker search, you can limit the search to just the Applications folder by using the menu under the search field (on the far right).

Command Line - Find
In Terminal, you can use the find command:

find /Applications/foo.app -type f -name "bar"


Replace foo.app with the name of your app, and replace "bar" with the name of the file you want to search for. 

If you want to search all apps in /Applications, leave out the /foo.app part of the command.

If you want to include folders, remove -type f, if you want to search only for folders, change -type f to -type d. You can also use the * wildcard in your filename to get partially matching results.