I tend to get 2-3 everstones each "run" in team magma's cave pretty consistently. I'm using a quagsire with thief (not PP maxed) and recover. I stay until thief runs out of pp or I faint, rest, come back. Seems to be about one run every 20-30 minutes depending on how attentive I am and how often my quagsire can't run from the wild pokes.
Best guess would be anywhere from 80k-150k per hour. Bad luck and being slow can make it way worse. Being quick and lucky can make it better. I think everstones > shards atm.
EDIT2: Also a quick note on island runs. A level 100 adamant persian can 1hko almost anything with slash. Here's my strategy: Have persian with Payday/Slash/Water Pulse/Shadow Ball. Have your HM Slaves, and also brink a miltank with Milk Drink or at minimum a poke with Wish. (Just fight a wild poke and wish the persian back to a healthy hp amount.) Payday the pokes that have low base defense, slash the rest, and use water pulse on rock/steel types while shadow balling psychic types. Use milk drink after battles to regain HP if one of the bird keeper's fking dodrios used endeavor or something. My persian has never fainted while doing this and I rarely run out of PP. (Also, the ground types with no normal resist tend to get 1hko'd by payday. They tend to be over lvl 56 too.) I also usually bring a starmie for the double battles.
If you learn which pokes get 1hko'd by payday, it becomes pretty easy to simply never run out of PP assuming you've maxed payday and slash. Just use starmie on all but 1 of the rock types in each hiker battle.