Probably overkill. Try:

sub Trueonce::TIESCALAR {
        my $s=1;
        bless \$s, $_[0];
}
sub Trueonce::FETCH {
        my($self)=@_;
        local $_=$$self;
        $$self=0;
        return $_;
}
sub Trueonce::STORE {}
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Include the code above in your program somewhere early, and use it like this:

tie $f, "Trueonce";
print $f, "\n";   # 1
print $f, "\n";   # 0 
print $f, "\n";   # 0
print $f, "\n";   # 0
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For some reason I'm in a tie() mood today...