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Although it seems odd that there is a "prohibition" against asking people not to bring you gifts when all you are trying to do is be thoughtful, there is a reason. The moment you mention gifts, you put an emphasis on gifts, which is the opposite of your intent. This is true whether or not this is your first wedding or an encore wedding.
Actually, friends and family who have attended a first wedding and given a gift are under no obligation to give another wedding gift to the same person, even if (as is usually the case) the new marriage is to a different person. There will be many who are happy to know this but who will want to give you a gift anyway, as a way to share in the celebration of your happiness.
The best way to assure them that you don't need a thing, but care deeply about their presence, is to tell them. You can also solicit the help of your attendants, parents, siblings, and other close friends by asking them to pass this message along to anyone who asks them what you would like.
New friends who have never given you a wedding gift before may want to give you something. For them, it is helpful either if you register at a few stores for the fun things that you don't have or make a list for your parents and attendants to share, if asked.
Your ideas could be anything from a new monogrammed towels and sheets, to a bunch of movie tickets and a popcorn gift certificate for a nearby theater, to a welcome mat for your front door. You can keep your ideas to reasonably priced items that would be fun for your friends to find or create to commemorate your marriage.