This has recently got a whole lot easier. PATCH is now implemented (like POST) in HTTP::Message.
First, update the HTTP::Message module (to 6.13 or later).
Then
my %fields = ( title => 'something', body => something else');
my $ua = LWP::UserAgent->new();
my $request = HTTP::Request::Common::PATCH( $url, [ %fields ] );
my $response = $ua->request($request);
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