The Name Your Price plugin extension lets you be flexible in what price you are willing to accept for selected products. You can use this plugin to accept donations or to take a new approach to selling products. You can suggest a price to your customers and optionally enforce a minimum acceptable price, or leave it entirely in the hands of the customer.
Name Your Price supports CoCart since

​
Add item to cart

Apply the customers requested price for the product when adding item to cart.
cURL
curl -X POST https://your-store.com/wp-json/cocart/v2/cart/add-item \
-H "Content-Type: application/json" \
-d '{
    "id": "129",
    "quantity": "1",
    "item_data": {
        "nyp": 24
    }
}'