You would do best with skinned egglayer for domestic leather production for simple setups. Turkeys are best domestic animals available, while ostriches are best overall (1 higher max, and 90k body size - 50% larger than dwarves). 40 egglayer strong turkey farm can produce 960 leather a year, and several times that in bones, meat, tallow.
More exotically, you could put creatures on chain to have them breed, then tear apart the children. A timed release mechanism could even ensure the children are fully-grown first.
I have seen mentions of serrated blade traps being effective dicing weapons. Though you'd need to obviously slice them into 4 pieces even with triplets born to match turkeys.
Hydras, having 7 heads, would be ideal.
However, either way, you can then reanimate the untanned hide and slice it into smaller pieces. Though note that pieces can get too small for weapon or bare-handed attacks to properly slay them (and I think only obsidian or ice casting would preserve the hide for tanning, of which ice is the only one that you can remove with mechanisms), so careful planning need to go into automating this, lest you risk your fortress.
Or you could buy leather from caravan. Starting at 5 a piece, and maxing out at 50 for maximum-priority(x2) elephant (x5) leather it's not expensive at all - you could buy 100 dog leather for a single masterful spiked wooden ball.
And the caravans will bring you hundreds of leather when maxing all of it out. Could produce shoes, trousers and cloaks for whole population several times over.
And yeah, they don't degrade, unless hit in combat in 43.04+ - only leather clothing degrades. Though I personally leave off backbags in my drafts, as that loses the happy thoughts from dining in awesome rooms and gives potential of storing backbag in a room and having food in it rot.