Is it okay to request to do a reading project with a professor at a later time if he had politely denied it before?
Yes, it is fine to ask. 

However, if you want to increase your chances that he will agree, make it a formal and specific proposal with stated goals. In other words, make it easy for him to say yes and to create criteria for your evaluation. Say what things you will deliver at the end. 

That way, even if he is busy, he might just decide that you won't add enough to his work to cause issues elsewhere.