It does not look like JSON::RPC::Client does 2.0, I found JSON::RPC::Common on CPAN which appears to, here is a code snippet for that:

#!/usr/bin/perl

use strict;
use warnings;
use Data::Dumper;
use JSON::RPC::Common::Marshal::HTTP;
use LWP::UserAgent;

my $ua = LWP::UserAgent->new;

my $req_data = {
        jsonrpc => "2.0",
        method  => "user.authenticate",
        id      => "xxx",
        params  => { user=>'yyy', password=>'zzz' },
};
my $req_obj = JSON::RPC::Common::Procedure::Call->inflate($req_data);

my $m = JSON::RPC::Common::Marshal::HTTP->new;
my $req = $m->call_to_request($req_obj);
$req->uri('http://zabbix/api_jsonrpc.php');

my $res = $ua->request($req);

my $res_obj = $m->response_to_result($res);
print Dumper($res_obj);
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