From a strict etiquette perspective, the kindest thing you could do is to talk him out of including the card at all. But this is not necessarily something you want to tell your father-in-law!
Etiquette bans mentioning gifts, even to refuse them, because, on any festive occasion, the guest of honor's mind is supposed to be on the wonderful company provided by the guests, not on the more tangible tokens that they may bring. In circles where weddings are popularly seen as occasions for lavish gift-giving, this can lead to awkward feelings for people who don't want their friends and family to feel "obligated." So what can your father-in-law do?
First, consider whether it's possible to talk him out of a firm "no gifts" statement. If he is likely to be swayed by being shown the etiquette rules in Emily Post or Miss Manners, go to the library and bring them home!
Convincing him that "no gifts" is incorrect still doesn't solve his problem of feeling awkward about receiving gifts, of course. One answer is to simply accept things gracefully, on the theory that guests give because they wish to. Another answer is to register for relatively low-cost items (and spread registry information by word of mouth), in hope that people will realize that, when the most expensive item on the registry costs $40, that's an appropriate maximum size for a wedding present. A third answer is to respond to all "what would you like?" inquiries with "We really don't want gifts-just your presence!"
In the end, of course, he and his bride will still have to contend with gifts! They can give them to other people as Christmas presents (being careful not to send the gift back to the original giver), donate them to charity, or whatever they like.
What if your father-in-law positively won't be convinced to leave out the "no gifts" card? There are a few situations where a compassionate exception is called for - a couple that is about to give away all their possessions and join the Peace Corps, an elderly couple in a nursing home where "more stuff" just can't be used or stored, and, possibly, a father-in-law who will do it his way with or without your help.
The most graceful option in this awkward situation is to make the message as discreet as possible. Choose the smallest size of card available-it need be no larger than a typical business card. You can have printed on it the simple message "No gifts." Or, if that seems cold and unfriendly, you can construct a longer message along the lines of "Your presence with us on our wedding day means a great deal to us. We wish to receive no other gifts."
Finally, everyone concerned should bear in mind that, if this is the second wedding for both the bride and the groom, they may receive few or no gifts regardless of whether they specify "no gifts." Many communities continue the older custom of not giving gifts for second or subsequent marriages, especially if the couple is clearly "established' in life.
One more last-ditch attempt to head your father-in-law off from the "no gifts" faux pas! Since this is a second wedding and thus presumably not following all the customs of a typical first wedding, he and his bride may have a special one-time dispensation to declare this a "theme" wedding of some sort and specify, in the invitation, a desired gift that is inherently sentimental and very inexpensive.
The appeal of a "theme" like this is that it allows friends and relatives to feel that they're giving generously to help the couple start a home together, but the giving is routed into channels that call for creativity rather than cash. It's most appropriate for a middle-aged couple that has everything-including friends who are old enough to have some wisdom to share! The cleverness of the theme allows the couple to squeak past the etiquette faux pas of mentioning gifts at all.
If your father-in-law decides to go this route, simply phrase the enclosure card something like this: "The most important gift you can give us is support in making our marriage grow. To symbolize that thought, the only tangible gift we desire is a packet of seeds that we can plant together and think of you."