Conversion of CO2 to methane
Let's take a close look at what the reaction entails. You want to convert $\ce{CO_2}$ to $\ce{CH_4}$ using $\ce{H^+}$. It is possible that the hydrogen ion will co-ordinate with $\ce{CO_2}$ to produce $\ce{[CO_2H]^+}$. 

Unfortunately it is very unlikely to have a second hydrogen ion attaching to the same oxygen to produce $\ce{[CO_2H_2]^{2+}}$. Now for the impossible step of water leaving and producing $\ce{[CO]^{2+}}$. This step would require a large amount of energy and $\ce{[CO]^{2+}}$ would be extremely reactive. Since it is highly charged, you would not have any hydrogen ions approaching the moiety. 

At this point, any further progress towards $\ce{CH_4}$ is fantasy. To stabilize the reaction, you need to add electrons to the carbon (which you don't have a source).