Since they were made in the image of God, and not born of woman, there’s no need for them to have the vestiges of umbilical cords. Usually when I see depictions of them in Renaissance art, their genetalia AND navels are covered by arms, hands or strategically placed flora. We assume genetalia because of modesty, and the Cain and Abel thing. But is there something… missing?
But in regards to your question about navels (I’ll assume they did exist for the moment), I guess there would be no way to check since Adam & Eve are long gone. Paintings would be up to the artist’s guess. As Cecil suggested, they would not need to have once (considering that a bellybutton is a scar from the umbilical cord…which they did not have). But I suppose God could have created Adam & Eve with bullybuttons in order to match their children in appearance. And then there’s the question of Man being created in God’s image (perhaps all humans are supposed to have navels in order to match the correct image, or perhaps the naval is a scar on the correct image). It may be a matter of faith.
Cecil says that most animals have navels. But what about those animals that are clones? I don’t have a clone nearby so I can’t use Cecil’s advice and inspect the animal.