Mahamrityunjaya mantra is the best choice but it should be chanted in continuous manner accompanied by homam and abhishekam if problem is severe. Along with this, Sri Rudram should also chanted as much as possible. One has to visualize the energy of the mantra entering into the patient and healing him.
Mrityunjaya mantra is as follows,
As per Mantra-Mahodadhi Chapter 16,
Up to three nakshatras from the birth nakshatra, one has to perform homam with samidha (wood) of Guduchi to avoid diseases and untimely death. 46.47
Performing daily homam with Durva is said to be the best for avoiding untimely death and for fulfilling all the desired. 47-48
For curing fever, one has to perform homam with samidhA of apAmarga plant.
For fulfilling all desires, one has to perform homam with guduchi pieces soaked in milk for one month. 48-49
To sum up, homam should be done with guduchi and durva grass. Abhishekam should be done with articles like milk, yogurt, sugarcane juice, water, etc.
For the homam one has to ideally do 10,000 oblations.