i use car seat 'hammocks' from ebay, theres a variety of strengths in the >
fabric and fastener area< of them. A lot depends on the weight of your dog, mines 31kg & i dont use them as a hammock, I cut 2 of them into seperate halves and use one part as a back cover and the second for the seat.....depends on what dog you have but they are quite big things and as far as i can tell waterproof...
http://ebay.eu/1PlYGClThese are the ones i buy & use but cutting them up to your design so they fit back & seat is down to each individual user
http://bit.do/bFboJ.