Your family members can only come to Greece with a tourist visa, like any other foreigner, which lasts up to three months.
However, in case you are in Greece with a residence permit for the acquisition of a medical specialty, which is certified by a special certificate from a nursing institution, your family members - after their relevant application - receive an individual residence permit, which expires at the same time as yours. The same applies if you are participating in research programs or have come for scientific research purposes.