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He actually means it and being pestered about it will end up irritating him and could sour things for you both. Just say something like: "Okay, maybe another time then", or "No problems. It'll keep until you're free." He'll appreciate the lack of pressure and the willingness to change your plans for him. Leave off asking him again for at least a week. That way, you won't seem pushy or desperate. For example, if he says he has already seen a movie or doesn't like the genre you've suggested, have one or two different ones to offer instead. Or, switch from movies to skating/a sports game/dinner out, etc. Be ready with flexible options.  Other possibilities include going to the park, the beach, out of town, etc. Another option is to ask him what he'd rather do. However, it's a good idea to offer your ideas first, to show you've really thought about this. He does need to think about it. This does not mean he is not interested in you; it means he needs to think about the activity. Feel free to say something like: "Sure, no worries. If you do want to, maybe you can let me know by tomorrow/Friday/the weekend, so that I can book tickets/reserve the seats/etc.". That's a good way of him dumping you. There are plenty of other times to ask again. If he keeps declining your suggestions, it's a good idea to ask him what he'd rather do. If you feel you can't ever make suggestions, you might need to rethink the viability of the relationship, as all relationships are about give and take.
If he says he is really busy, don't push it. If he says no because he doesn't like what you've suggested, be ready with an alternative. If he says he needs to think about your suggestion, take it at face value. Don't force him.