Yaupon Holly, Southern Wax Myrtle, Chinese photinia (not red tip) can be trained into a tree. The 4 feet of planting space is a challenge especially if you don't want it to hang over the fence into their yard. I have a similar situation where my neighbor can look out their kitchen window over the sink into our bathroom. Not so bad in the summer/winter as there is frosted glass, but in spring and fall when we have windows open can be kind of embarrassing for them. They finally put a nice rose of sharon to block the view since they had more room to plant something.

Thanks for the suggestions. It's a rent house with a very large backyard so I am not too concerned about it hanging over. I'll take a look at your suggestions. Which of these grows the fastest?

Yaupon Holly is the only one I have, and it's pretty fast. I'd get the largest pot size you can - probably 1 - 2 would be plenty for a 10 foot wide screen. It's still going to take some time. Could you put a lattice extension on top of your fence at that point and put a fast growing vine on it? Only problem with fast growing vines is they tend to be a maintenance challenge, but it could be temporary until your trees fill in. That would probably be the fastest though.

I would strongly recommend attaching lattice to the top of the fence and getting a vine to grow there. Look for something evergreen like Carolina Jessamine. I think the area is too narrow for any kind of small tree unless you went with something like Italian cypress, but those get way too tall for what you need and will eventually get about three feet or more across. I look at it this way. It is a rent house. You probably won't stay there long enough to get any benefit from planting a large shrub / small tree since no matter what kind you plant, it will take a few years for it to grow and fill out properly to create the screen.

Nandina. Good vertical growth, evergreen. A lot cheaper than a tree for a home you don't If I read correctly you need 3' of height. If that is the case some of the more refined varieties of nandina that stay shorter would be an outstanding choice.

If you're going to go with a vine, Lady Banks Rose if you get enough sun. Evergreen, thornless, grows like a weed, blooms once in the spring. At 3' it wouldn't need a trellis probably it would make a mound that high