Goodyear tires

I purchased a set of Goodyear Eagle HTR's from Tirerack two months ago and they are directionals. I was having a pretty good vibration from the driver side front tire so I had the shop rebalance the tire. Still, it was vibrating pretty good at highway speeds. They said the tire was oblong and was basically junk. I got a new tire from Tirerack with absolutely no problems getting an exchange. Anyway, this one is doing the same, but not as bad. The other 3 are smooth as silk but this one still vibrates around 65 mph and up. I wanted to ask your opinions on what the standard psi should be with our tires. I realize with more air pressure the more bumps and vibrating will be more noticeable. I wanted to go down on the psi and see if that helped at all. What is the recommended psi for our tires? I know what it says under our trunk lids but that makes the tires look pretty flat-looking.