Traditions apart, it is the availability ,and price that will determine this now.
Any oil which does not give out much smoke, which stays for a longer time, and does not irritate the eyes of people in the place will suit the purpose.
Generally Gingelly oil is used.Due to the cost factor nowadays Ghee is used on very few special occasions.
In Kerala "Vilakkennai" is available which is cheaper is used sometimes.
Coconut oil does not stay for long and dries up soon .
Earlier days , when the " மை" is used as eye liner , the soot from ghee oil lamp and gingelly oil lamp were preferred for their quality.
Now when lamps are lighted only for decorative show, all these do not matter.