I'd imagine I could find out if I chop every tree down in my town, then buy a sapling from Leif and plant one tree a day, and then shake every adult tree every day until I get the same amount of stuff two days in a row. After that I'd just have to chop an adult tree down and the three growing trees.
Well, according to the this guide I found that for New Leaf they report that each day, 20 trees produce bells, 2 trees produce furniture and 5 trees have beehives.
But since furniture, beehives and bugs can also fall from non-fruit trees, I guess you would need to have at-least 30 trees. I've never seen an exact counting as it probably varies from day to day due to the random nature of the non-bell drops.