Liquid Nails is a brand name, you have to pick the right product within the brand. You'd be talking an epoxy, of which you could use any brand. Not easy to use or apply and the cost, I'd guess $100 or more if you're doing the entire outside. If you wanted to go with a glue a cheaper choice would be a polyurethane glue. Still not cheap, but way less than epoxy. It takes a long time for glues to hold something heavy like a rock, so you need a way to keep the rock in place. Not fun.
The issue with glues is how long they last. The glue itself may last forever, but the zinc its adhered to not so long. The glue doesn't protect the zinc and instead traps water against it. It oxidizes and comes apart. It only takes a layer one molecule deep to fail. I've seen this with clear silicone inside plastic filters where a black fungus or bacteria layer grew between the silicone and plastic tank. Only lasted about 6 months.
I don't know how long a glue would hold to zinc. Could be a year, could be 10 years. But I wouldn't be surprised to see some failure after a year. Of course you could repair failures.