There are lots of different ways in the rabbit language to show happiness. The ears will be in a less tense position than a scared rabbit, and many rabbits shake their heads and make their ears wobble or flap when they are happy. This can develop into a twist of the whole body, usually whilst jumping in the air - known as a binky. These look very funny to watch, and a rabbit that is happy will run around the room jumping and twisting like mad.
A rabbit that is happy but sleepy will lie down in a relaxed position - the harder the position is to get up quickly from, the more relaxed the rabbit is. A rabbit lying on its front with back legs under it can get up instantly, and isn't as relaxed as one that is lying stretched out on its side with its feet sticking out behind it. This is a much harder position to run away from quickly, and shows that the rabbit is very relaxed and feels safe. If your rabbit lies down near you like this, it must be very comfortable with you, and feel that you are no threat whatsoever to it.