Hard to understand your question. The counter ic's are already in existence. You just want to select one that has all your requirements, including the negative edge trigger. It's all part of the spec sheet on the device, and is generally part of the one-line device description.
S papabravo said, adding a 74xx04 to the input will invert the trigger, and make a positive-edge trigger device go on a negative signal. Sometimes it takes an understanding that you can always get the logic to perform the function you wish.