Carbon dioxide is not the only thing causing climate change - but it is the most important factor, and it is the only way that the numbers work.
11 years is a half cycle. ~22 years is the cycle. We have just come through a an unusually low minimum of sun spot activity, and the sun's output is lower when there is low sun spot activity. This is actually counterintuitive since sunspots themselves are much cooler than the rest of the surface of the sun.
Here's an excellent NOVA program on the Sun that aired earlier this year:
NOVA | Secrets of the Sun
As I understand it, the sun is increasing its output over the very long term - but the output over the short term can drop off, and it does drop off during sun spot minimums. The most well know minimum was the Maunder Minimum.