eval {
    require Module;
    Module->import;
    1
} or do {
    require Module::Core;
    Module::Core->import;
};
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Possibly wrapped in a BEGIN block.

Some modules already do that, see e.g. JSON::MaybeXS.

This is one use case of Module::Load::Conditional which is itself a core module.

Addendum: Having gone searching for something even more intuitive I have found Best which does exactly what you are after. Even though it isn't a core module, the docs include a section for coping with that. Perhaps this combination approach will serve you well.

One way to do this is:

BEGIN {
    unless ( eval 'use DesiredModule; 1' ) {
        require AlternateModule;
        AlternateModule->import();
    }
}
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However, I've also made the argument that using two different modules is not necessarily the best approach. There's ways to get modules onto systems where you don't have permissions (local::lib or even App::FatPacker), plus if you're going to be writing your own module anyway, why not just always use that?

Updates: Added the ->import call, as per choroba's post. It's often not required for OO modules. If you need to pass a specific import list, you can do eval 'use DesiredModule qw/some_func other_func/; 1' and AlternateModule->import(qw/some_func other_func/);. Another possible variation is that you can replace the inner block require ... ->import(); with eval 'use AlternateModule; 1' or die $@||'unknown error';. Stringy eval is often the wrong choice, but in this case it's fine because it's using a fixed string of code.

Not specifically useful for this case maybe but also check out the if module to conditionally load a module.

thx for your quick and helpful responses!

I'll try out all of them