On pencil branches do a simple wedge graft -- angled cuts on both sides. It is easier than cleft or T so first try on a couple random shoots and after a couple tests you should be good to go.

Note that it is very difficult to get multiple grafts on a persimmon, the tree will often stop feeding one and it will die in favor of others. Persimmons are unique in this regard. I had three grafts of Wye Maru on different trees made the previous spring and all died this spring because the trees didn't want to feed them (one was in fact the only growth on that rootstock, even after two months of knocking off all sprouts I could not get the graft to grow more than two inches!).

If you do want to try make sure to graft all at the exact same height and be religious for the next two months about knocking off any sprouts. This spring I managed to get four varieties going on one large stock (about 3" diameter main trunk) but the dratted root put out a sprout about 5' away that I did not notice for a long time and the grafts were starting to die when I found and pulled it (the sprout was already 5' tall when I found it!). Those varieties have not grown at all since then and I expect I will have them all dead and the tree sprouting from the roots next spring.

Scott

Hey Scott, thanks for the advice. By the way, how far up from the ground level should the grafted site be? 1 or 2 ft up from the ground?

Tony

Put it wherever is most convenient to get them all at the same height. I did my recent 4-way at about 2' off the ground.

Scott

Scott, Thank you. I let you know next summer how the graft hold up.

Tony

Tony - good advice, above, from Scott.
I do almost exclusively bark grafts anymore -see Joe Real's tutorial, linked below - it's how I graft everything from persimmons & pears to pecans & oaks; it's really sort of a modified T-bud placement, if you think about it, but instead of a budshield, you're inserting a stick of budwood into a T where the horizontal cut is just a decapitating cut.
But, I've done simple splice grafts, 4-flap, whip & tongue on persimmon with reasonable success. All are best done after the rootstock begins leafing out and the bark 'slips'.
Aftercare, as Scott described, being diligent in keeping new shoots from the seedling understock rubbed off is THE most important part of grafting persimmons.
Multi-grafting persimmon can be done, but it's harder to manage with this genus than just grafting onto a single stem - but if you have the time to religiously keep an eye on it, rub off adventitious shoots and keep the grafts growing in balance, you should be able to pull it off.

One caveat - persimmons 'self-prune'. As the tree gets taller, lower limbs decline and are shed off. So...be aware that if any particular variety you graft on has a higher placement and becomes the dominant leader, varieties grafted(or that just end up) lower on the tree may 'disappear' over a period of years.

Lucky, you forgot the link.

Lucky, thanks. Remember to show us the link from Joe Real's tutorial as mentioned above by Brandon.

Tony

Oops. Well, I did forget the link, didn't I? Sorry.
Here 'tis...

Here is a link that might be useful: Joe Real's bark-grafting tutorial