This is just my opinion, but I hope that it will hold some insight for you.
In regards to the current meta and possible counters to it, there are no 100% counters.
One of the biggest variables in every game of League you play is the enemy teams skill/teamwork. No two teams play the same and no two players will respond to different situations in the same manner.
Many players have become accustomed to the current meta game of sending-
1 Bruiser type solo Top
1 AP caster/nuker/assassin Mid
1 Ranged AD carry and 1 Support Bot
This team composition has been found to be not only the most efficient, but to provide in a typical game the highest chance for success.
This does not however mean it will always result in a win for the team that uses this format.
One of the reasons for this is that with set lane compositions, you often know who you will be facing in lane before you ever get there. This allows for strategies and tactics for each lane to be devised before you ever encounter your enemy in the lane.
Teams that decide to try something different, whether its sending that AP caster/nuker bot with your AD carry, not having a jungle so that your bruiser top is no longer going to get zoned out by that counter pick, sending your tank mid, all of these things can not only confuse the enemy team, but they can put them out of their comfort zone.
Being out of that comfort zone, not knowing how to deal with that dual top lane or that tank that you just can't seem to do anything to mid, can majorly screw with a player and a team's mindset.
Counters to the meta that I have seen be effective were not always necessarily fantastic teams that just switched up where a specific role goes. Part of the game of League of Legends is the mental aspect to it. A team that can confuse, agitate, or otherwise just throw off the shackles of what the enemy expects them to do, can win games regardless of filling those typical meta roles.
I have personally seen teams of tanks, teams of assassins, teams of AD carries and teams of champions that would typically be viewed as supports just roll the enemy team. Not because their team composition was better, but because they were able to change the flow of the game. They were able to force the enemy team to deal with situations that they normally would not find themselves in, fighting champions that they may very well not know how to play against.
The biggest thing with these teams, regardless of their team composition is that they are able to take control of the game. When they gained an advantage, they kept it. They push, gank, go for dragon/baron when they can take it, ward and communicate with their team. They "know" what they need to do to win, and they also know that they often times have to win before the game goes on to long.
In conclusion, although there is no "hard" counter to the current meta, with proper knowledge of the game, a little bit of innovation and a whole lot of teamwork, it is "possible" to win with something other than the current meta. (You just have to try!)