Yes - I had excactly the same issue. Here is how I resolved it:

In the DB module:

#!/usr/bin/perl -w
use strict;
use warnings;
use Class::DBI;

package AvalancheDB;

our $DBPath="avalanchedata.sqlite"; # Default file nme

our $DBH;

sub import{
   my ($class,$newpath)=@_;
   $DBPath = $newpath || $DBPath;
   #print "IMPORT: Setting path to '$DBPath'  \n\t \n";
   ## Delay this setting till AFTER IMPORT !!
   AvalancheDB::DBI->connection(qq|dbi:SQLite:dbname=$DBPath|, "", "")
      or die "Cannot connect to Database at $DBPath;";
}
...
[download]

In the MAIN code...

...
my $ProgramDir;
BEGIN{
   ($ProgramDir) = ( $0=~m|(.+)\/.+$|, $0=~m|(.+)\\.+$| ,".");
}
use lib ( $ProgramDir, ); # Current Program's Dir
use AvalancheDB ("$ProgramDir/avalanchedata.sqlite");
...
[download]

Basically, I'm (ab)using the "import" function to get the DB path.