It looks like a fairly standard D-Pad membrane to me. It's just a piece of rubber with conductive disks on the bottom that connect the board electrical contacts when you press down. Any place that sells replacements parts for a controller or device with a D-Pad should have a part that'll do. Just make sure they're roughly the same size (http://wiki.surkow.com/File:Gcwzero-parts-measurements.jpg
) or you'll have to make fit adjustments.
The easy solution is to steal one from somewhere else like a broken game controller or other devices. Otherwise you'll have to purchase one. A quick google and ebay didn't get me terribly far and iFixit was out of stock on similar parts for XBox controllers. They seem to be called membranes, pads, or gaskets interchangeably.
They sell silicone button+membrane (same piece) parts here for the original gameboy: http://store.kitsch-bent.com/product/silicone-buttons
If you really wanted just the membrane you could probably use an exacto knife to remove most of the button part so it'll fit under the Zero's DPad button. Although they also list a slightly cheaper 'membrane set' so maybe that's the right part.
Here are some generic ones on eBay: http://www.ebay.com/itm/Lot-2-New-Button-Switch-Pad-Replacement-for-Xbox-360-Controller-/111626533835
I hear that disassembly/reassembly of the Zero can be a bit finicky in terms of losing the battery connections, etc. So, be careful I guess. (http://wiki.surkow.com/GCW_Zero_Disassembly
) I would suggest testing that the buttons work before you close it up again, but that may be difficult, so maybe it'd be easier to open it up again if you have any problems.