Diamonds start showing up in the granite zone (the layer right after ice), but they're still a bit rare there. If you're trying to farm diamonds for the Omnishard, that’s the earliest place you'll start seeing them.
Between Scoot and Grampshell, go with Scoot if you're running into stamina issues in the lower layers. Grampshell is a better pick if you're a bit more comfortable managing stamina and want to be a little greedier.