You could store the fruit in the fridge, unless you have lower quality fruit in there that you use for cooking. Unfortunately, multiple refrigerators all use the same "inventory" when placed on a lot (i.e. If you put a meal in a fridge in the kitchen, you can pull it out of a different fridge in the basement). But if it was your desire to keep the perfect fruit separate from the stuff you cook with, you could use a treasure chest. And if you place multiple chests on the lot, they will all have their own separate inventory.
And in case you're unaware: you can move an entire "stack" of items from your sim's personal inventory. If you notice, the left hand corner of each item is a "tab," and if you click your mouse there and hold it, you can move the whole group of items. This also works for the family inventory (or simply placing things on the floor from personal inventory), and you can place multiple items out in the lot this way. When your finished (if you still have items left), simply click the Esc key to end the process.