[beza1e1]

Nearly correct. POST does not specify the name of the resource. So you do

  /orders/42 # with { order: { paid: true  } }

And it returns the /orders/42/payment transaction resource.

[drsim]

I disagree. Surely an Order HAS Payments, therefore /orders/42/payment POST is more correct. Likewise orders/42/shipment.

Nicely leading on to /orders/42/payments/1.