Doesn't descent into baby directories, finds files named list.dat ... modify to what you need

#!/usr/bin/perl --
use strict; use warnings;
use Data::Dump qw/ dd /;
use File::Find::Rule qw/  rule find /;

my $thisdir = shift ;
my $nobaby = rule( directory => name => 'baby', 'prune' );
my $list   = rule( file => name => 'list.dat', );
my @files  = find( not => $nobaby , or => $list, in => $thisdir, );
dd( \@files );
__END__

$ tree -f -a coy
coy
|-- coy/abu
|   `-- coy/abu/list.dat
|-- coy/baby
|   `-- coy/baby/list.dat
`-- coy/dabie
    `-- coy/dabie/list.dat

3 directories, 3 files

$ perl fffindrule.pl
["coy/abu/list.dat", "coy/dabie/list.dat"]
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