There is no current way to organize your items currently. Hopefully the game will implement it in a future update!! The only way I've seemed to be able to organize stuff (bugs, fish, fruit, etc..) is to use them all or sell/list them all off. Then collect them in the order you'd like them in your inventory. Also if the item you want next in your inventory isn't spawned for you, you can always buy it from a friend's Market Box.
I hope that my answer helped you out!!