It will depend quite a lot on what kind of safety valve(s) the tank has, some kinds, like the small 20-ish pound tanks for barbecues can be transported safely in any position, some of the tanks like you describe (probably 100 pound) are designed to stand at all times, the float inside might release the gas if on the side.
Also, make sure you can in fact transport it in a passenger car, the propane stations around here post signs on the maximum weight of propane a passenger car can transport and I think it's way less than 100 pounds, probably just 2-3 tanks of 20 pounds each. You may have to call a commercial place to either refill the tank for you or bring you a filled up tank and swap for yours.
Good luck!