The carrier can only be installed during the initial POST, and not with subsequent PUT requests. When creating a shipment, and you want to designate the carrier, you must send a POST request using json body, for example:
[ { "id": 1, "order_id": 115, "customer_id": 0, "order_address_id": 16, "date_created": "Wed, 19 Dec 2012 17:17:10 +0000", "tracking_number": "111222333444", "shipping_method": "None", "shipping_provider": "fedex", "tracking_carrier": "fedex", "comments": "A sample shipment for order 115", "billing_address": { "first_name": "Louise", "last_name": "Dean", "company": "Skiptube", "street_1": "147 Meadow Vale Way", "street_2": "", "city": "Fullerton", "state": "Rhode Island", "zip": "74674", "country": "United States", "country_iso2": "US", "phone": "7-(086)085-9448", "email": "" }, "shipping_address": { "first_name": "Louise", "last_name": "Dean", "company": "Skiptube", "street_1": "147 Meadow Vale Way", "street_2": "", "city": "Fullerton", "state": "Rhode Island", "zip": "74674", "country": "United States", "country_iso2": "US", "phone": "7-(086)085-9448", "email": "" }, "items": [ { "order_product_id": 16, "product_id": 0, "quantity": 1 } ] } ]