Strategy, lots of strategy.

As someone previously suggested, debuffs may help, sure, Kakuzu can dispel them, Earth can dispel them, but that doesn't leave them invincible to them. Especially if you kill Kakuzu early on or throw the debuffs onto them post-Kakuzu, which is decently easy to achieve if they have more initiative.

Power is a big factor, if they have...lets say 20k more then you....good luck.

10k is more reasonable, but if it's just a couple thousand, they can be beaten.

"Everything has a weakness"

From the looks of it, they have a round 1 Konan-Kisame team, you could attempt to stop their earth main, effectively stopping the Konan for a round (Due to the fact that that Kisame, even if his barrier comes into play and the sharks die, and eventually provide enough chakra), it affects both sides, thus no mysteries can be played.

Indeed....hmm

Speaking of which, what kind of team do you use? I know that you're looking for counters for this team, but if you're seeking them out to help yourself, wouldn't it help to know what kind of team you already use, or ninja you have?

Regardless, teams are indeed a major factor.