You are going to have to do heavy lifting here still, with the auth/authz steps and managing the tokens and the user agent and the actual requests and response parsing, but this should get you over your first hurdle–

#!/usr/bin/env perl
use strictures;
use HTTP::Request::Common;
use JSON;
use URI;

my $endpoint = URI->new("https://www.googleapis.com/batch");

my %writer = ( emailAddress => 'example@appsrocks.com',
               role => "writer",
               type => "user" );

my %domain = ( reader => "appsrocks.com",
               role => "reader",
               type => "domain" );

my $request1 = POST "https://some.uri/you/must/construct",
    Authorization => "Bearer MOOOOOOOKEN",
    Content_Type  => "application/json; charset=UTF-8",
    Content       => encode_json(\%writer);

my $request2 = POST "https://some.uri/you/must/also/construct",
    Authorization => "Bearer MOOOOOOOKEN",
    Content_Type  => "application/json; charset=UTF-8",
    Content       => encode_json(\%domain);

my $top = POST $endpoint,
    Accept => "gzip",
    User_Agent => "YourMomsCooking/0.00001";

$top->add_part( $request1, $request2 );

# Here, you would pass the request to a WWW::Mechanize object or somes
+uch.
print $top->as_string;
[download]

Related reading: HTTP::Request::Common, URI, JSON, HTTP::Message, and WWW::Mechanize. (Update: added URI refs.)