You need at least two documents to get nagarikta,

Nagarikta of your father and  your birth certificate. You should apply for nagarikta in the district office of the place you were born. for example if you were born in kaski you have to appl;y in kaski district office not in Kathmandu.

If you parrents dont have Nagarikta 
They should get nagarikta from the place they were born. They have to go to the district office of the place they were born and apply for it. It is not unusal for older people to apply for nagarikta in Nepal. Many people do it. You parents may have some relatives, or the people who know your parrents. So, "Ga. bi. Sa" secretary or in case of "Nagarpalika" "woda" secretary may have to certify for it.According to law it is not necessary for your mother to have nagarikta for you to apply for it. But Your father must have nagarikta. If both of them dont have it, and dont want to apply for it ( very strange). Why your parrent dont want to get nagarikta? they dont want their kid to have nagarikta of nepal? what is the reason? Parrents help kids a lot. You parrents should help you to get nagarikta.

If your parrents are from kathmandu valley it may not be that difficult for your parrents to get citizenship. but out side kathmandu valley they may ask for bribe.

After your parrents get "nagarikta" then you can apply for it, It may take up to one months ( depending upon the situation) for your pparrents to get "nagarikta" but once they get their Nagarkta , for you it may take only a day or two to get Nagarikta.It is not necessary for both parents have nagarikta.  But it is very important for your father to have "Nagarikta".