From my own personal experience, I think I can offer some helpful advice to him. Like him, my wife and I also have struggled at times with abstinence and have been resentful toward NFP. And we too consummated our marriage about two weeks after our wedding day.
In my opinion, however, the problem lies not with NFP. If it did, I think NFP would not have lasted for the 18 years of their marriage. The problem is with the way this man and his wife treat each other and their attitudes toward sex. Using phrases like "ask for sex" and "earn sex" are very revealing. It's as if sex is a treat for the husband if he's a "good boy" and it's a chore for his wife that she must grudgingly perform if he's earned the right to it. The wife's rolling of the eyes when the request for sexual intercourse comes up betrays at the same time a very understandable feeling of being used as well as a callousness toward her husband's needs.
For the woman, I would suggest Dr. Laura Schlessinger's book, The Proper Care and Feeding of Husbands, especially the chapter on sex. It has done wonders for my wife and me and has helped her understand what I as a man had been going through.
For the man, I can tell you that abstinence is 10 times harder when we give into the sexual stimuli that assault us on a daily basis. Women in revealing clothing, risqué ads on TV and in print, readily available pornography on the Internet, etc. all contribute to an environment that makes abstinence intolerable and chastity almost impossible to live. By God's abundant grace through prayer and the sacraments, men are able to resist temptations that would raise our passions and make us unfaithful to our beautiful brides — even in thought.
On a more practical note, some ways of reducing abstinence might be to deal with the PMS from which his wife is suffering. The book Fertility, Cycles and Nutrition from CCL is a great place to start. For my wife and me, we're into our 12th year of almost continuous infertility brought about by pregnancy and breastfeeding. Another child may or may not be possible for this couple but it's worth pointing out: Being generous in the service of life does have its advantages.
This couple is in our prayers that they will see NFP for what it really is: a blessing of God in their marriage.