I don't know how to specify that MyModule.pm needs to be generated from MyModule.eyp using the command line

I think you shouldn't need to specify that, nobody but the author of a distribution needs to run or have installed eyapp

But anyway, you could use search.cpan.org/perldoc/ExtUtils::MakeMaker#PL_FILES

WriteMakefile( 
PL_FILES => {
  'bin/doEyaAp.PL' => 'lib/MyModule.pm'
  'bin/doEyaAp.PL' => 'lib/MyModule.pm'
},
[download]

Or MY::postamble, example in http://cpansearch.perl.org/src/CASIANO/Parse-Eyapp-1.182/Makefile.PL but note 1) its not portable  PERL5LIB=lib; perl ... use $(PERL) -Ilib ... instead and 2) its an author specific target, make publicdist

I'm sure dzil also offers some support for this, but I don't need Maximum Overkil