Is there ever any new items in the second hand shop?

Yes new items come to the shop once you get enough trainer points I believe. When my second hand shop got new items I think i was somewhere between 1,500-2,000 but less points may be required idk. Stardust is a material for most of the new items.

The second hand shop, or Mr. R's shop, will get new items later on in the game. Most of the new items will require Stardust. You can get the new items by winning the Nintendo Cups. Also, like drakclowd115 said, you can get enough trainer points to trigger it.

I think it's every month

it isnt every month i unlocked somethings a little while ago (maybe 800 points or less ago actually) and now i have 5900 points. ive had the game for less than a month and i recently unlocked rainbow disc and lure and some other things. :-) but of course there will be heaps more to come. also more TP's ago i unlocked koopa chair and rainbow wig and birhtday cake hat and some other things. :-) hope this helps u.

Just so you know, all places where you can buy something get new items eventually. Every day in a row you play the game, or every time you reach a certain amount of trainer points, a new item is added somewhere. The secondhand shop is no exception.