Both actions are subject to a three year statute of limitations. See N.C.G.S. § 1-52(5). The statute of limitations appears to start running when the extramarital relationship is discovered.

The elements of alienation of affections in North Carolina are:
(1) a marriage;

(2) a genuine love and affection existed between the spouses;

(3) the love and affection existing between the spouses was alienated and destroyed; and

(4) the wrongful and malicious acts of the defendant caused the loss and alienation of such love and affection.
Litchfield v. Cox, 266 N.C. 622, 623, 146 S.E.2d 641 (1966).

While the second element can be met in marriages that are less than stable, the fourth element cannot be met unless the third party's acts are malicious. (Even when you know the other person is married it can be a defense to argue that there was no intent to alienate affections within the marriage, although that's probably a risky defense.)

It is my understanding that to prevail in a criminal conversation lawsuit you would have to prove the following three elements:
1. You, the innocent spouse, are legally married to the adulterous spouse;

2. One or more acts of sexual intercourse occured between your spouse and a third party; and

3. That the adulterous act (or acts) occurred within the three-year statute of limitations.
The only defense to a criminal conversation suit, once those elements are satisfied, is that the innocent spouse consented to or encouraged the adultery before it took place.