it depends on how far the tree itself is from the spot. I figured out, that the most problem with tree shade is competition of the tree with your plants. Because you said it is midday shade, I take it the tree is close to the spot and gives shade directly down at mid day. And none of the plants like competition. But if the spot gets at least 6-8 hours of sun you are OK with almost any plant if you solve the competition problem(containers? extra watering and feeding?)I had several large trees around my garden. The garden was OK, but not great. We removed most of them - the difference is noticeable. Actually, I just noticed you are up for fruit as well. Yes, there is one that loves midday shade and do not mind competition of the trees that much. Black Currant.(Black only, as red, pink and white need full sun). It is a great berry bush, that can give you few pounds of very aromatic berries and has a very fragrant leaves that can be used in teas or for pickling. Berries have a large amount of vitamin C. They can be frozen as well. USDA Zones 4-9. It could be restricted in some areas due to the very old laws related to common rust disease with white pine that was money maker at the time law was introduced. Now days all black currants sold are rust resistant, but some nurseries still restrict shipping to some areas. The law is per town, so you can check if your town is restricted or not. Even if it is, you always can buy it on e-bay and will never have trouble with it because you planted it. It is just very slow law machine.

Zucchini does ok in part shade (at least 4 hours of strong sun), as does winter squash like acorn or pumpkins, but it won't be as sweet. Bush beans, peas, carrots. You can even grow tomatoes in part shade contrary to what you read... they just won't produce as well.

I don't have any experience growing under a tree, but I imagine you'd want to make a raised bed, or stick to containers.

If it gets 6 hours of non-morning sun you can grow anything.... Peppers and eggplants are the biggest sun lovers.

greens do best in part shade. Spinach, chard, collard, lacinato, kale, lettuce, radicchio, cardoon, arugula, mustard greens, and so on and so forth.

For "part shade" it makes a big difference how partial the shade is. If it's many hours of blocking the sun at midday, no one will like it. An hour or two, no big deal, really. Also, note that "shade" itself is a relative term. I have a bed on the west side of a house, so it gets direct sun half the day. It's "shaded" by the house in the morning. BUT, that bed sees the sky the whole day, and so gets a lot of light. No problems with any crops there. A tree that makes it dark underneath it will be a lot worse. Be aware that the sun is significantly brighter when it is higher in the sky. So an hour of sunlight blocked at noon is a lot more detrimental than an hour of sun blocked at 4pm.

Now, when you dig in your bed, do you run into a lot of tree roots? If you do, then the tree is competing for that soil. If you don't run into a lot of tree roots, then you're good to go.

It probably depends on what type of tree but, I am in a zone similar to yours (zone 6, mountains of central New Mexico). My season is somewhat short but we go from cool to hot very quickly and so I use some of the shaded areas around my juniper tree for things that benefit from a break from the heat. Last year's experiment was with celery root (celeriac). It did beautifully planted on the east side of the tree. That is also where I plant strawberries. Of course, greens are good there. Lettuce will take longer to bolt if it has a break from the sun. Rhubarb is another candidate. I am sure other ideas will come to me after I hit send.

Awesome, thanks for all of the responses. It looks like I'll have to figure out someway to measure out exactly how much sun the plants would miss out on underneath the tree. The tree itself is fairly small (15-20ft tall I'd guess). It's some type of stone fruit tree, but I haven't owned the house long enough to see it produce, so I don't know whether it's peaches, apricots, or something else. I do look forward to the fruit, so I wouldn't want to put anything in the ground that's going to compete heavily with the tree.

I'm liking the idea of putting a black currant in the ground, and some greens in containers, if it's not too late to make that happen here. I'm pretty sure I've already missed out on peas, but that's a cool idea for next year.

Either way, I'm glad to hear that there are some ways to make use of that space. Thanks again!

you can buy black currant in the pot . I bought mine around same time 2 years ago as a tiny bare root plant, this year I should have berries - at least it is flowering like crazy. The seller I bought it from is not there anymore, but here is another one: Black currant on e-bay

some trees (mulberries, maples) have invasive roots. They'll grow into you bed quickly and the next year you may have the bed fool of roots. Vegetables and most of the other plants can't win this competition.

no, collard, cardoon and radicchio will give you a good crop, even if it is many hours of shade. They are my rotation in certain beds that have become full shade over time.