The two things that you could use against a false accusation are..
.. and you already used both of these in your initial encounter. You tried to tell him it wasn't yours and you offered to get your newpapers out of the trash as proof, but he just spoke over you.
However, the encounter you had was clouded by his anger. Likely he had gone over the encounter in his head a few times before he came to your door. He may not have heard what you said because he either expected you to deny it and had already decided this would be false, or he just heard what he wanted to hear.
If you want to attempt to put this right you may wish to approach him in a day or two when he has calmed down. He will probably not be expecting this and so hopefully will not be in an angry state of mind.
I wanted to talk to you about what happened the other day. I can
understand why someone else's trash in your yard would make you upset,
but I want you to know, it really wasn't mine. It wasn't my newspaper
and I definitely wouldn't throw trash in someone else's yard.
See what he says. Ideally he will accept what you say, and you may even get an apology. However, if he doesn't accept it or becomes hostile again you could just say:
The fact is that you can ask everybody in this neighbourhood if they
saw me throw a newspaper in your yard and you won't find a single one,
because I didn't do it. But I bet a few of them saw and heard you
throw it at my door. If you come to my home in a threatening manner
again or throw anything at my property, I will report you to the
That really puts things in perspective. He did something wrong when he threw it at your door, and you could likely prove it. But hopefully it won't come to that.