wowza,
now that's a challenging dilemma.
the first thing that pops into my mind is seed sowing, such as morning glory seed or another type of vine that can easily be grown from seed.

the second thought is containers - long metal containers that could sit right on top of the wall cap .
You'd probably have to have them custom made .
You could alternate the heights of the planters too to break up the run of the wall.

third thought is a living wall . They are getting to be pretty common theses days. You could do it with succulents and bromeliads.

and the last thought I had was hanging baskets mounted from the 4x4 posts. Or a combination of hanging baskets and planter boxes on top of the wall caps.

Why not trying to cut out some windows in the fence, so you can see the green stuff behind it or to pick the neighbors oranges? Stained glass or some other opaque glass will provide privacy and let the "Outside in".

You must certainly know that 2 inches (!) isn't space to grow anything. Even if you get seeds to sow there, you have to water them, and then you're just watering the weeds and, well, really, it's just silly.

You must focus on container gardening. Which is fun. Enjoy.

One big problem you're going to have is that if you do get anything to grow across that fence successfully, you will be sweeping leaf litter and dead petals off your bench seating - continually!

I'm not sure why you're going to all the trouble to install a drip system for such an inhospitable gardening area, unless it's set up just to water pots and containers? In that case, I'd set nice large pots on the benches (with suitable waterproof overflow saucers underneath), instead of trying to balance a container upon a too-small ledge.

BTW, the fence would look a lot nicer cleaned and restained. A few pieces of colorful garden art hung up, and the whole could be made into a cohesive and attractive design, with great urban privacy.

Thanks all for the helpful suggestions. The drip line will be for containers. That fence is over one hundred feet long and I won't be cleaning or doing anything with it anytime soon. I do agree it is ugly...which is why I'm trying to think of ways to distract from it--lol. PS: What is a living wall?

I think it is entirely rational to plant in that area, rather than using containers... two words: root zone. The ground can offer so much more nourishment, moisture, and space to plants than a container can (even if you are technically borrowing it...).

Seeds are a good way to start, but also, when I mail order clematis I get them in a two-inch plug size. They bulk up nicely in time. Annual vines bought in small pots could also be squished in there and would grow over the space in a season. What I would spend some money on is nice pieces of trellis to enable the vines to get up the fence to the lattice part. Or you could just string fishing line; that's a taste issue.

It should be noted that vines will technically leave the ground area empty, so a ground cover, annual or perennial, is a good idea. Then you wouldn't need containers, although if like me you have a pathological need to buy them, they could still be accommodated with ground cover peeping out in between.

Just don't plant anything your neighbours would consider noxious.

Hanging baskets, also a good idea.

KarinL

Morning glories and zinnias. Would make it beautiful

Love it! ...I would find a local metal artist and have them create a large (4'x8' at least) metal sculpture -- or start scouting for one that's already made. Make sure that it will stand out -- unfortunately your sun is not standing out from the fence. It's also a bit small -- go for impact (go BIG!).

Luckily, your pallet looks pretty neutral, so almost any color would work -- except brown or black. Make a statement.

If you install the sculpture along the wall, you will have virtually no maintenance -- fill the 2" wide space with pebbles instead.

Have fun!

Heidi