Play ranked and ban him, sorry theres no reliable way to counter him in 3v3 especially blind pick.

Play malphite I guess, with somebody that can carry

End the game by the 30 min mark.

There r a lot of chars that can shut tryn down with varying effectiveness but it only works during the laning phase u can extend it some what by keeping control of dragon lizard extra and stop him from feeding off ur team, with common sense and some judicial warding but sooner or later he will get the money up and buy his way into monster-hood as some mentioned there r some chars that can go toe to toe and come out ahead jax noc nasus rammus but depending on the players and situation I find that that alone is nothing but meeting force with = force and can go either way. I prefer to work on systematically destroying his base as it starts to be hard to stop his farming so that by the time ur going in to take down their nexus turret assuming they haven't surrendered ur not facing a fully fed tryn. Heh guess it sounds pretentious but I think the best key to countering an effective tryn is not letting the game go late since hes a late game char.

In order to successfully counter a skilled tryndamere you need good coordination and team work. Its a 3v3 some champs arent meant to be fought 1v1. Try using Teemos Blind and his speed to counter tryndamere or champs like: Swain, Malz, Riven, Wukong. A champion with an escape/CC or DOT to counter his "endless rage" ability and some well timed ganks should leave him useless

SpearShot panth destroys tryndamere spear-run-spear-run-spear-stun

there is no counter to trynd in 3v3 your best bet is to try your best for 15 minutes then surrender

Champs that counter Tryn


Lee Sin
Malphite
Nasus
Fizz
AD Sion
Teemo
Swain (must land nevermove)
Mord
Shaco


Just run ignite on most of your champs. Get an executioners calling on AD champs. GG I never have a problem with him and I never play him.

Best counter : GP/Panth.
Insane poke on him.

thornmail won't cut it.
TBH not much will in TT except constant cc and a lot of armor, and even then its still an uphill battle.
Not the answer your looking for im sure, but there really is no "do this and win" answer, at least not for 3v3 tryn. To be honest the map is imbalanced. No way else to really put it.

New Jax can handle Tryndamere pretty well, seeing how you can negate 2 seconds of auto attacks and then stun him. With the rest of your team backing you up, and using exhaust, there shouldn't be too many Tryndamere's you cannot handle.
Also, common items that counter AD champs include any that give tons of armor and or a attack speed debuff. Items like frozen heart, randuin's, and (the already mentioned) thornmail all fill this role.
One last idea is to make sure your team comp has hard CC in it anyway. This helps with any enemy champ that gets out of line, Tryndamere or otherwise (except Olaf).