- Improving growing conditions only contributes minimally to your cherry tree's fruit size
- Your neighbour's tree has a genetic advantage over your tree in terms of fruit size
- You can bud graft a branch from your neighbour's tree onto yours
- The best time to do this is from July 15 to August 15
- Your own tree should have bark that slips easily
- The other tree should have mature buds
- Grafting the branch from your neighbour's tree should lead to bigger fruit on that branch only
Just some background
So I have an apple tree in my back garden. I had heard as a child that you could
graft pear tree branches onto apple trees and forever have a branch that grows pears. Thus, a few days ago, I started researching this. Apparently, most commercially bought apple trees are not grown from seeds but from grafting. That is, someone gets a mature apple tree branch and grafts it onto a small (dwarf) tree. Just so you know for your own research, the tree that you intend to graft another fruit tree onto is known as the rootstock whilst the thing that is grafted onto the rootstock is known as the scion. For apple and pear trees, the whole process can be simple as making a diagonal cut on the root stock and scion, jamming them together and securing with electrical tape (whip graft).
What type of grafting should I use for cherry trees?
As for cherry trees, you should (according to this useful page from the University of Minnesota) employ budding which is:
a form of grafting in which a single bud is used as the scion rather than a section of stem. It is the most commonly used method for fruit tree production in the nursery, but can also be used for topworking plum, cherry, apricots, and peach as well as young apple and pear trees. (Cherry, plum, apricot, and peach are not easily cleft grafted or whip grafted.)
As for when you should do this...
Budding is done in the summer, usually from July 15 to August 15, when the bark of the stock slips easily and when there are well-grown buds. The first step is to cut bud sticks of the desired cultivar from strong shoots of the present season's growth (see A in Figure 6). These buds should be mature, as indicated by a slightly brownish color.
.. which makes your post very timely.
Some fruit trees don't self-pollinate, but it seems like your neighbour's cherry tree doesn't have this problem.
What influences cherry size on different trees?
If you're interested in why your cherry tree has smaller fruit than your neighbours, there's a (free access) paper from the Journal of the American Society for Horticultural Science (JASHS) that links the size of your cherries to the number of (mesocarp, i.e., the fleshy bit) cells in a cherry. Let me quote their abstract. I'll also write my interpretation of it:
Mesocarp cell number was the major contributor to the differences in fruit equatorial diameter among the five sweet cherry cultivars. The cultivars fell into three significantly different cell number classes: ≈28 cells, ≈45 cells, and ≈78 cells per radial mesocarp section. Furthermore, mesocarp cell number was remarkably stable and virtually unaffected by the environment as neither growing location nor physiological factors that reduced final fruit size significantly altered the cell numbers.
Growing conditions don't significantly alter the number of mesocarp cells.
Cell length was also significantly different among the cultivars, but failed to contribute to the overall difference in fruit size. Cell length was significantly influenced by the environment, indicating that cultural practices that maximize mesocarp cell size should be used to achieve a cultivar's fruit size potential.
You can increase the size of each cell, but the major influencing factor of cherry growing is the number of mesocarp cells.
Following the above section, what comes next will probably only have minimal contribution to your cherry tree's fruit size.
You can investigate whether your cherry tree has the right growing conditions. If your neighbour's tree is making nice cherries, its rootstock may cope better with the surrounding soil (in terms of acidity, etc) - in which case, transplanting his cherry branch to yours won't be as useful as you think. Assuming you've not done this, the solution to nicer cherries may be as simple as the application of compost or the adjustment of soil pH.
See this post for more information on grafting.
Sometimes you hear of people severely cutting back the number of growing fruits so that nutrients are less spread out, giving larger but less fruit. This will probably work to some extent on your cherry tree in conjunction with what is written above...