wowdb has some decent data for many of the 5.4 pets now (some of it is from PTR I'm sure, but nobody has reported any changes to drop rates so it should be reliable).
The Timeless Isle pets all have good numbers by now; the rare pets from rare mobs seem to be in the 2-3.5% range, while the uncommon pets from rare mobs are more like 5%. The rare pets from regular elites (Jademist Dancer, Ominous Flame) are 0.4% with a large sample size, so this should be pretty accurate (ie it's super unlikely to be any higher than 0.5%).
Bonkers is 1-2% from the Timeless Chests -- the sample size is pretty large, but there are multiple objects called 'Timeless Chest', and it's not clear to me if they are exclusively Bonkers-dropping chests (ie this data might possibly be contaminated with non-Bonkers-dropping chests, which would artificially lower the apparent drop rate).
There's a similar issue with Lil' Bling -- he's listed as a 0.01% drop chance from Blingtron Gift Packages, but, this data is likely to be contaminated with Gift Packages that were opened pre-patch (similar to how the initial drop rate for Battle Stones seemed really low, because the data included pre-5.1 pet bags that never had battlestones). Anyway, Lil' Bling is trending sharply downward and there's tons of them available, so they can't be very rare.
For SoO pets there's understandably less data, so these are much more uncertain. Sha of Pride is the only pet-dropping boss with a decent number of kills. Gooey Sha-ling is listed at 0.7%, while Droplet of Y'Shaarj is listed as '???' (ie it was not seen in the recorded kills). This doesn't mean anybody should panic about Viscous Horror-type scarcity, but it does mean the droprate is likely to be pretty low.
*edit* semi-related: Jadefire Spirit and Ominous Flame are P/S, Lil Bling is S/S, but everything else has multiple breeds. In particular Bonkers has 5 (P, S, H/P, P/S, H/S), which will make it tough to get the one you want, especially as he's non-tradeable. Droplet of Y'Shaarj has at least 3 breeds (P, P/S, P/B), and possibly more, there aren't enough out there to know for sure.
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