Stationery, whether it's good or not, is a stationary object. If you turn it into a paper airplane, the stationery is no longer stationary.
So stationery involves writing materials, and stationary involves motion, or the lack of it.
I looked it up and found that, in the 1700s “stationery wares” were sold by “stationers.” These people stayed in one place to sell their wares (thus making them stationary, in a way). They were frequently booksellers who also sold writing wares. At some point, the spellings diverged into stationery (meaning writing wares) and stationary (meaning fixed and unmoving).
One web site says to remember paper (with the "e") to differentiate the two. Another says to use envelope to remember the "e".
Remember: Never use good stationery while riding a stationary bike; you'll sweat it up.
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