Just declare the enum outside the bounds of the class. Like this:
public enum card_suits
{
Clubs,
Hearts,
Spades,
Diamonds
}
public class Card
{
...
}
Remember that an enum is a type. You might also consider putting the enum in its own file if it's going to be used by other classes. (You're programming a card game and the suit is a very important attribute of the card that, in well-structured code, will need to be accessible by a number of classes.)