if you want to go directly,there are 2 options
take a TNSTC bus from nagercoil,or get a triweekly train
if you want to break your journey, go to madurai mattuthavani bus stand from nagarcoil via virudhnagar and get an overnight bus to rmm
if going by road,you need to come to nagercoil by local bus as there are less buses from kanniyakumari
personally...
more... i would prefer the triweekly train
if going by train,dont forget to wake up at 4:45 to see the grand old pamban bridge