how much sun to you get there? and have you had the PH tested? for sun, you could try irises (the old purple 'flags' live in boggy conditions) and Irish Moss might work as well...for shade, I think that the cinnimon fern's the most tolerant of alkaline soil.

Digging down to the concrete, and putting a barrier down (we used Thompson's Water Seal in one case, but that's NOT the recommended useage for it- maybe just plastic?) and adding acidic elements (coffee grounds, oak or pine dross, 'holly-tone', etc) should make that more productive.

I have a dry spot like yours- there's only 5 inches of dirt there, and I have nasturiums growing merrily there....but they don't like wet feet.

heck- if it's enclosed, plant mint there, and let it take over- you'll jsut have to shear/harvest it when it starts getting too leggy!

Annuals? Cacti/succulents/sedum?

You wrote, "concrete underneath and wet". Does it _stay_ wet? If so, you have a perfect set up for a bog garden. WOW!
Some gardeners go to lots of trouble to make a bog. Reeds, iris, grasses, and unbelievably gorgeous flowering perennials will be available to you.
Do a "bog garden" search, and be watchful for things that work in your zone-9.
Here's to mud in your garden!

I thought bog garden too,