One wrinkle on broquaint's kludge is its interaction with an import subroutine.
'use'ing a module normally goes through:

BEGIN
import
INIT

However, adding an import subroutine to the above code produces:

BEGIN
INIT
import

One possible workaround for this would be to move any INIT code to the end of the import subroutine. Yet even this is not a 100% solution as:

use testpkg ();
[download]

causes the import subroutine - and hence the moved INIT code - not be be executed.

For the module I'm writing, I have a BEGIN block, an import subroutine, and an INIT block. The INIT block consists of just one function call. Therefore, I warn the user that if they want delayed evaluation of my module, they must do so as follow:

eval {
    require MyModule;
    import MyModule qw/.../;
    MyModule::MyInit();
}
[download]