I am assuming that your cousin was born in a country that is not eligible for the lottery. If so then the answer is no. She will not be ligible for the lottery through Singapore even though she has now become a singaporean citizen.But,
But, if she is married to somebody born in Singapore or some other country eligible for the lottery then she can apply through the country of her husband. [This is in addition to the application her husband is allowed]
On the other hand if her country of birth is eligible for the lottery then she is eligible through her country of birth, even though she may not be a citizen of it any more.
There are some other very marginal cases where a person can claim eligibility through a country where he/she was not born. For those, just refer the new DV2009 instructions when they come out.