Grape has been finished this year already but persimmons are available from 20th October to 30th November.
- Fruits Oukoku Yasaka
Grape is until the end of October and pears are until the end of November.
* You'll have to book either by phone or web (http://www.fruits-oukoku.jp/contact.html).
Kanko Noen Nanrakuen
Grape and pears available until early October. Tangerines are going to be available from 5th October.
More places are listed here:
Hope these help you!
Fruit picking in autumn is persimmons, tangerines, grapes, etc.
I found a page for information about seasonal fruits.
This page seems to be useful for gathering information about fruit picking in Kansai region.