#!/usr/bin/env perl
use Data::Dumper;
print Dumper(\@INC);
print "$_\n" for glob '/usr/local/bin/amos-3.1.0-rc1/lib'
[download]

jdilts@jdilts-VirtualBox:~$ perl datadumper.pl 
$VAR1 = [
          '/usr/local/bin/amos-3.1.0-rc1/lib',
          '/usr/local/bin/amos-3.1.0-rc1/lib/AMOS',
          '/usr/local/bin/amos-3.1.0-rc1/src/PerlModules',
          '/home/jdilts/perl5/lib/perl5/i686-linux-gnu-thread-multi-64
+int',
          '/home/jdilts/perl5/lib/perl5/i686-linux-gnu-thread-multi-64
+int',
          '/home/jdilts/perl5/lib/perl5',
          '/etc/perl',
          '/usr/local/lib/perl/5.14.2',
          '/usr/local/share/perl/5.14.2',
          '/usr/lib/perl5',
          '/usr/share/perl5',
          '/usr/lib/perl/5.14',
          '/usr/share/perl/5.14',
          '/usr/local/lib/site_perl',
          '.'
        ];
/usr/local/bin/amos-3.1.-rc1/lib
[download]

I meant to post this code, with the * at the end of glob, to list all contents of your lib dir (don't forget readmore tags):

#!/usr/bin/env perl
use Data::Dumper;
print Dumper(\@INC);
print "$_\n" for glob '/usr/local/bin/amos-3.1.0-rc1/lib/*'
[download]

I also tried putting the .pm in the /etc/perl directory.

Did you put AmosLib.pm in /etc/perl/AMOS/?

No, but I will give it a try.