I didn't get it to work yet and will post later when I've solved it.

alright with the following code I got it to work.
Thanks!

sub create_external_inv {
    my $agent   = HTTP::Tiny->new;
    my $headers = {
        Accept         => "application/json",
        'Content-Type' => "application/json",
        Authorization =>
"Bearer 123"
    };

    my $url =
      "https://moneybird.com/api/v2/123/external_sales_invoices";

    my $data = {
        external_sales_invoice => {
            "reference"          => "M-8426",
            "date"               => "2020-03-14",
            "contact_id"         => 456,
            "details_attributes" => [
                {
                    "description"       => "coffee",
                    "price"             => 2.25,
                    "tax_rate_id"       => 891,
                }
            ]
        }
    };

    my $res =
      $agent->post(
        $url => { content => to_json($data), headers => $headers } );

    print Dumper $res;
    if ( $res->{success} ) {
        print "Okay!\n";
    }
    else {
        print "\n\nNope...\n\n";
    }
}
[download]

The results print okay!.