Several problems here. Some are just typos, I think. For example you have "%keys %METHODS"; presumably you just mean "keys %METHODS". Another is you have "*$methods" where presumably you mean "$method".

But the main problem is that you need to set up your %METHODS hash in the BEGIN block, so that it gets initialized *before* you try to use it. Ie.:

    my(%METHODS);
    our @EXPORT;

    BEGIN {
        %METHODS = (
            foo => 'bar',
            bo  => 'baz',
        );

        @EXPORT = keys %METHODS;

        foreach my $method (keys %METHODS) {
            no strict 'refs';
            *$methods = sub {
                return $METHODS{ $method };
            };
        }
    }
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