You are not supposed to be a carry as the Support. That is why it is called Support. Wish more people realized this.
I mean, who can't climb with Janna?
If you can't carry as a support then you're doing it wrong.
Any role has the ability to "carry" a game. Granted, as a support it does require a bit more effort from your team, however assuming all things equal, you absolutely CAN and SHOULD be able to carry from the support role.
During laning-phase if you make the right grab/land a stun or otherwise catch the enemy adc or support out of position even slightly then it can be a free kill/double kill. Carrying the lane is simple if you're a quality support and assuming your adc is even mediocre.
Mid game/late game - simply catching someone out, or picking the right target in a team fight or otherwise disrupting their coordination with a well placed stun/hook/root/etc will help your chances greatly.
The basic rules of playing support are the same as every other role: You won't be able to carry eveyr game regardless of how well you play, but the better you play the higher your chances of carrying games. Your teammates won't always follow up, but as long as you continue to set up opportunities for them then you should be good. Ward, keep warding and don't stop warding :).
Support is the hardest role to learn, but the easiest role to play once you have learned it... if that makes sense. Yes, there are frustrating aspects to it and I hope Riot addresses them eventually, but overall if you're a good support there is no reason why you can't carry games.
The problem as I see it is that as a community we have different definitions of carry and carrying and also many do not differentiate between the two. Riot has addressed this by changing the class ADC into Marksmen. Personally my view is this, Some one who was carrying or carried a game should be called the MVP rather then the carry. A carry champion is one who theoretically will end up making the most impact on winning a match but in practice this is not always the case. Further complicating things is the theory of hard carrying. Hard Carrying is winning with your individual impact compensating for teammates having negative impact. Its like being in a relay race and 2 folks on your team have injured them self's so you said screw it, picked them up and ran their section of the race. Then because your so darn burly and quick despite the added weight of the folks your carrying you still cross the finish line first and to the dismay of the enemy team the way the rules are set up your win was perfectly legal so your team gets to keep the gold medal despite the fact it was not much of a team effort.
Anyhow bit off topic near the ended there so i will sayIf your impact in what ever form of gameplay was the highest factor on your team destroying nexus or forcing a FF then you carried your team even if your not on a carry champion. If your on the losing team, even as a carry champion the loss means its not a game you carried. If you did you would have had a victory.
Note, I really think we should endeavor to make more distinction between carry and who carried, look at how goofy this next sentence is.
The enemy AD Carry won because I as a top lane carry couldn't carry my un-carryable and badly balanced team of Late game carries who also could not carry any of their other carrys as well as the enemy carrys did because their jungle fking hard carried his team of trash carrys.
Tldr: Some one who carried is in my book just the mvp of the winning team. Losing team has no one who "carried" so they lost, even if they had a team full of carry's. This is determined to me by looking at their impact on the game not kda or damage.
Edit, moved the Tldr around to be more visible and bolded it.