First off, please enjoy this chart that I found: https://docs.google.com/spreadsheets/d/1x7C6rhO0KHRIs1SBBLPvuTVbsFmuTtR3zB99XMMJ8yU/edit#gid=140485586
Thresh/Caitlyn - Thresh's hook, at lvl 5 with 45% cdr, assuming you hit the one before, has a 3.6 second cooldown and lasts for 1.5 seconds. Caitlyn's traps take 1.1 seconds to activate, so with proper placement you can easily snare immediately after thresh hook ends. That snare lasts 2 seconds. With a thresh flay in between to fill up the .1 second gap (and possibly caitlyn e for slow, or more traps surrounding for minimal escape routes), you can then hook again and repeat. The only real delay will be timing his flay, and the delay in his hook cast. However, if caitlyn traps again right in front/behind, thresh's flay can knock them into that trap for another 2 seconds. Caityln's traps, even without cdr, will be up often enough for more repeats than you will need.
Thresh/Blitzcrank - Another fun one, that I'm sure you've tried if you enjoy messing around, is blitz + thresh. Thresh hook, then blitz hook, followed by immediate knock up, followed by thresh flay, followed by another thresh hook. Missing .6 seconds if you don't include flay. The great thing though is blitz R for silence so they can't flash or dash out during the .6 seconds, and thresh's flay will have a brief pull and a slow so they definitely will not get away especially without flashes/dashes. This one is especially fun because of the unexpected damage of those abilities + blitz passive goes off for free and thresh's e passive makes the 1 auto he can get off very potent. Not infinite, but a very very painful 3 seconds with no counterplay, and a very strong possibility between the slow and silence for at least one repeat if needed. If you're bot lane as you mentioned, that damage should be enough for many supports and all adc's.
Fiddlesticks/Maokai - Fiddlesticks is a fun one to do this with as well, try fiddlesticks and maokai. The fids E silence can be used to fill the brief gap (not quite infinite cc, but very close and a slow/silence will fill the gap) so they can't dash or flash away. Fids Q, Maokai W, maokai Q + fids E, Maokai E for more slows + damage. The problem with this one is the mana dependency. 2 second root every 4.95 seconds. 2.25 second fear every 6.05 seconds. Also very solid if lead with Maokai W, then Fids Q, then the rest again. Shorter gap between abilities for the first repeat.
Alistar/Nautilus - This I believe (I'd have to double check numbers) is permanent, but difficult due to alistar headbutt/q combo and nautilus long cast times and the pull of his q.
Leona/Morgana - Leona E: roots as travel, so basically just land it for free q. It supposedly lasts about .5 seconds. Q 1.25 second stun every 3.85. Morgana q: 3 seconds every 6.05. This means Q for 1.25 seconds on Leona, Q for morg for another 3, Q again on Leona for another 1.25 seconds, and you're missing 1.8 seconds in between. While this isn't an infinite rotation, you can get this rotation three times between Leona's E+R for one gap, and Morgana's R + leona E for the 2nd gap. Then another leona E after the 3rd gap, means a total of: 5.5*3 + 2(1.8 needed but both fills are 2)*2 + .5, 21 seconds of CC. Leona's E is up every 4.05 seconds so used as a filler between 5.5 seconds of CC shouldn't be a problem.
Morgana/Sion - Sion, 2 second channel of Q for 2.25 second knock up, goes on CD for 3.3 seconds after use, so need 3.05 seconds of CC before next usage goes off. He can also ult in between if need be, so can Morgana. Morgana I think works best, though leaves .05 seconds of escape potential, plus need VERY good timing. Hard slow on sion e helps during that time as well.
Poppy + Tahm Kench - Lets not forgot the trolliest of them all, Tahm Kench. Tahm Kench + Poppy is an absolutely godly combination. The hard part is how to get Tahm Kench passive stacks up. You can do this with a q slow of his, or a poppy stun if they get near terrain / on the wrong side of poppy to be pushed to tahm. Tahm q stun for 1.5 seconds once his passive is stacked, followed by swallow for 3 seconds, where he is able to put them exactly where poppy needs to ram them into terrain again for another 2 second stun every 5.5 seconds. Get his stacks up again (as swallow destroys them) and he can stun again for 1.5 seconds, every 3.3 seconds, then eat them and repeat. A slight variation is to start with tahm stun, don't eat them, and then have poppy stun if they're already near a wall. This allows for two of tahm's 1.5s stuns, with 1 of poppy's 2 second stun, for a total of 5 seconds, then eat them to fill the gap, and poppy will be able to stun again, followed by tahm, for a total CC time of: 11.5 seconds. Since Tahm's swallow is a 5.5 second cd, and there's another 3.5 seconds of stun afterward his first devour, it's not an infinite chain, but it is 11.5 seconds with only a 1.8 second gap between a repeat.
These are just some combo's that I think work well, try and mix and match as well. I know you asked for permanent CC, which is very difficult, but going along with your theme these combo's can either get you very close (or in some cases with perfect timing, on the nose), or be devastating damage wise with a ton of CC, and tons of fun to do.
In this vein as well, though not the same, is Trundle/Anivia. New anivia allows for much easier stuns to land, and you can block off the entire lane, and if done right, displace them in the process. They also have slows and plenty of damage.