One way would be to add your private module path before the CPAN module path in @INC so that Perl will prefer local module installations over installations from CPAN:
my $private_module_path = '/usr/local/myscript/lib';
unshift @INC, $private_module_path;
use Net::MyModule; # will pick up the first Net/MyModule.pm that is fo
+und in @INC
An alternative approach would be to load both modules and then try to find out which one has the largert version number, but that is a hairy thing to try and a user who does local modifications might not think of bumping the version number high enough.