2G and below are really small tanks, I usually recommend filters for small tanks at the least 3G. Sponge filters are best for bettas, especially in small tanks. This
is the sponge filter I use, but it's a little bit big and strong. I think most people use this
sponge filter. I recommend this one instead of mine... If it's still too strong, use a T valve to control current. In a tank likes yours, water changes are necessary 2-3 times a week anyway. The cycle wouldn't be that stable either; your choice, really. I think it's better for you to get a big tank like a 10G-20G. You would only have to do a water change once a week.