If morphine is not something that a patient would want, it is entirely possible for the patient to ask their doctor to provide a similar substitute. You may wish to also mention the effects that morphine gives you, and that you want to avoid them.
There are a variety of pain killers available. Discuss the different alternative options with your physician making sure to tell them about your aversion to morphine. Be open an honest so that there are no surprises. Depending on how invasive the surgery is, your options could include acetaminophen or other medicines that aren't as powerful as morphine.
The pain medication and anesthetic depends on whether or not you are allergic to other pain medications and your preference of said pain medicaions. If you do not have any allergies to pain medications your doctor will most likely perscripe either Darvocet or Percocet. This does vary according to standard procedures.
A hip replacement can cause pain for a few weeks, so most doctor's prescribe some sort of pain reliever to aid the patient. Generally, not morphine, though.
Morphine is a common pain relieved used after surgery, but you could ask to use dilaudid instead, which is similar to morphine. Just ask your preop nurse.
There are numerous analgesics. If you don't like morphine, then you must discuss other options with your physician. It would be good to discuss this prior to your surgery.