I don't think you can say «Can you place these books orderly on the shelf?». It would be like saying «He waved to me friendly». You can say "Can you place these books tidily on the shelf?" because "tidily" is an adverb derived from the adjective "tidy". However, "orderly" is an adjective derived from the noun "order" so you would have to say "Can you place these books on the shelf in an orderly way?".