I am considering turning the perpetual game into a monthly game and adding a daily game as well.
If I make these changes, the site will offer 3 game options. Daily, Bi-Weekly, Monthly.
Any thoughts?
The risk of losing coins when playing on daily game is higher...

I don't think many will play on your daily game.
How about if you add annually game?

When you think about it, the perpetual game is going about as well as an annual game. I think short term games may perform better.