I have done a little research into what ways of printing tends to last the longest. Laser printers are effective for longer term archival purposes because it is essentially baking a layer of plastic (toner) onto the paper, which is why the paper is warm when it comes out. As a result, laser ink would does not easily deteriorate or fade. An inkjet printer, on the other hand, sprays tiny droplets of liquid ink onto paper. Inkjet ink would be less resistant to moisture because it could bleed or run if the ink doesn't stay dry. However, higher quality ink and paper can help reduce that risk.
There are also thermal printers which uses heat-sensitive paper and selectively transfers an image to the sheet. One example of a thermal printer used for bitcoin is the Piper wallet, which is essentially a Raspberry Pi hooked up to a thermal printer. According to their FAQ, the image will last 20 years when stored in typical office filing conditions (In a cool, dry environment with no exposure to light).
http://cryptographi.com/pages/piper-faq
. We probably have all observed receipts fading to the point of being nearly unreadable within a year or so. Piper wallet uses a higher quality thermal paper so it's different than what you would get as a receipt from a store, but would still not be ideal for long term storage given the other options.
As with all things, whether you use Laser, Inkjet, or Thermal, the quality of the ink and paper matter greatly, as well as the conditions in which the paper is kept. Given that a private key on a physical bitcoin is going to be printed on a laser or inkjet printer, sealed under a hologram, and the coin stored in a plastic airtite case, flip, or slab, it would be reasonable to expect that any coin that does not get exposed to high level of moisture or temperature extremes would, at a minimum, last 80-100 years. If the maker uses high quality paper and ink/toner, then it should last much longer.
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. Congrats GP. 
