"Do you believe?" I think that would be something like Shinjiru ka（信じるか)? But it might also be Shinjiteiru ka? (are you believing?). "Can you believe" (I think) would be shinjirareru ka (信じられるか). I'm not quite sure if it matches the nuance that you want though.
Also, I used the plain form here...if you want a politer form, add -mas ~ます. So you would have shinjimaska 信じますか.
Anyways...I think that should be it...but definitely double check before using/ writing. (If I am wrong...please let me know...my japanese needs all the help it can get