Trying to hold down large tracts of China would surely see the British Empire close to being hopelessly overstretched.
As to OP, I think you need to concoct a situation in which the Rebels being in power is more significantly more advantageous to the Brits than maintaining the status quo and continuing to deal with the devil they know. Obviously, that wasn't the Taipings, with their puritanical fanaticism, blasphemous perversion of Christianity, and anti-Opium posturing.
If the Qing continue being stubborn, reneging on treaty provisions, treating the British as inferior barbarians, and there's a rebel group that's moderate, pro-Western, pro-trade etc, then maybe they start getting tempted. Though they'd presumably have to tread a very fine line to support the rebels whilst still trading in Qing territory and for most it probably wouldn't be worth the risk, as long as they're making their money (you could easily get a situation where some of the merchants are clandestinely supporting the rebels whilst British officialdom remains pro-Qing).
If the Qing are continually recalcitrant the Brits would eventually reach a point where helping depose the Qing in favour of a more open new regime becomes a better option than calling in the troops to clobber the Qing again and intimidate them into signing another treaty that'll just get subverted in a few years. I'm not sure exactly when British patience would run out in such a scenario, though.
I've seen it suggested (I cannot seem to find where, so treat this dubiously) that the Xianfeng Emperor (and/or his coterie of advisors led by Sushun) intended to repudiate the terms signed by Prince Gong to close the Second Opium War. This obviously didn't happen with Xianfeng's death and Cixi's subsequent coup but if it had that would have led to further deterioration in Anglo-Chinese relations, and much frustration on the British side. The British would also be somewhat perturbed if such a turn of events saw Gong, a man they've found reasonable and capable of working with, get disgraced or fall from favour.
Averting Cixi's coup and leaving the 8 Regents, led by Sushun, in charge could also by itself lead to frontier Anglo-Chinese relations, and make the installation of an alternate regime more appealing to the Brits.
Tweaking which British officials are present in China so you get someone who is vehemently anti-Qing and willing to consider intriguing with other groups could also be helpful- changed personalities on either side to create more friction and hostility between the Brits and the Chinese would be a necessary prerequisite for this scenario, as would a 'nice' rebel movement, and something making the status quo untenable.
Alternately, if the country absolutely goes to shit (to an even greater extent than IOTL) and the Qing are rendered impotent and absolutely incapable of anything resembling effective government, then maybe supporting a rebel group with the potential to restore order becomes appealing- absolute anarchy isn't great for trade, after all.
I'd also query what exactly we mean by "support"- there's something of a spectrum between arms shipments (which I think were a thing early on to the Taiping?), through "here's some officers to assist", to thousands of British troops marching alongside the rebels. The lower end of the spectrum is more plausible.
You could probably get a situation where the British are ambivalent, and freely trade with and provide arms to both sides (clandestinely or not), and then jump on the winning team when it's clear the Qing are finished.