Doubling bitcoins is possible but its pretty hard, with websites its without any doubts not possible but that is already clear.
With trading there are some options but it also has some big risks to be honest.
Currently the price of bitcoin start to increase and I have doubt that iy will once again double up in value so any person who will have their money in bitcoin will double up in a few months, and if someone want to double the amount of bitcoin then they should have to do trade.
I do not think that you can double your money in a period of 2 months and rely solely on price movements. because I think the prices will not grow more than 2-fold within two months? perhaps only a few percentage points?