These plants have been in the ground for two months.

Any suggestions?

Give up. Start planning for next year. Read as much as you can on how to amend your soil, "The Soil looks very rocky", or replacing it, Houston TX topsoil sellers. The reason for this harsh advice is even if you get these plants to an improved state I doubt you'll get much fruit production as you're entering a period where 100 degree days are normal so you'll likely have blossom drop.

Ahhh, no reason to give up on them in my opinion. Sure, you are going to hit the dead of summer down there, but as soon as september gets here, you will enter a beautiful pepper growing period. The rain will eventually stop down there and things will dry out. I would limit the waterings until your soil dries out down there. If you can keep them going over the next couple months, they will be primed to take off when the temps come back down a bit.

As for next year. When the growing season ends this winter, I would remove all of that mulch and then fill that raised garden to within an inch or two of the top with some nice rich soil and have it ready for next spring.

Nick - I'd start fertilizing with a water soluble fertilizer like Miracle grow. I also would add a heaping tablespoon of Epson Salts in with the Miracle grow watering can (1 gal size) solution when you water. Do this bi-weekly for a while. You should begin to see some growth and greening up...

Sandy

definitely no need to give up. I agree with esox and cut back on the watering a bit. I use a mix of compost for my plants so I typically don't need to add much in terms of fertilizer, but for peppers, any general tomato fertilizer should work.

I agree with esox and bmelz, no since in giving up unless you need the garden space. I'm in Texas and all of my hot peppers seem to produce more once the heat breaks anyhow. Blossom drop might be a blessing, because your plants can use their energy to grow, rather than fruit. I have had great results with Neptunes Harvest fish and seaweed liquid fertilizer, Miracle Grow will work too as sandy mentioned. Those plants look like they need some nitrogen.

Peppers are tough, you have plenty of time.