Scott is right, as usual.
My product preference for urine is Bac-Out digester.
Whatever you use, work on the rug back first. That is where the deposit is the most, and working from the front, the urine removal product you use must go through all of the top before it reaches the back.
And some rugs are simply not worth dealing with, depending on their value.
So... using what you have- I suggest first cleaning the back as well as you can. Then apply your product to the deposits in the back.
Let dwell for an hour or so- longer if possible, and consider rolling it up wet, and leaving for 24 hours, then re-clean the back, then do the same to the front.
And whatever product you use, pass the cost along to the customer, and list separately like- "2 gallons Odorcide @ $30.00 per gallon" or whatever, plus the regular cleaning fee you charge.
What about the floor the rug sits on? Wood? Carpet? I bet it is soaked, too, and must be dealt with in order to remove the odor.
Gary