Waist cinchers or nippers are still a common lingerie item. If you don't see them in your store's lingerie section (double check with the slips and girdles to be sure), try any of the many lingerie retailers online.
Absolutely! You may have to buy them online, but there are definitely still stores that sell them. You'd want to look in the older ladies sections. Other than that, I've heard two pairs of Spanx works well as a cincher.