It's a really easy solution, but harder to set up correctly. There are two options I use:
1. Flash guns, like the Canon and Nikon high powered models will sync at any shutter speed, but you lose distance. If you are doing one person portraits in that situation, you can make it work by getting closer to the subject and using high speed sync. That's one of the benefits of using the newer and strong flash guns. And don't worry about the flash being on the camera--it's only fill flash and that's a fine place for fill flash.
2. This is the solution I prefer, since it allows you to use all natural light: Set up a scrim, which is a translucent piece of cloth, to filter the direct sunlight. Doing such turns harsh noon light, or side light, into diffused light that looks like overcast--nice very soft transitions. You can buy thick or sheer nylon at a fabric store, or use large fold out or aluminum tube panels and fabric. There are many ways to mount and set it up, including complete store bought systems. After you get the scrim set up, set another reflector on the key light side and use that as a key light. I'll bet you won't believe your results. Beautiful lgiht in 12 Noon overhead summer hard light. If you have an assistant, or someone willing to hold the scrim for you, it makes it much easier. You can also use your flash gun on a stand as the key light to the left or right. The effect with today's flash guns is very good, but never as nice as natural, diffused light.
Here is a shot I took recently using an off camera bracket bounced up and angled to get a left side key look in an abandoned building, where natural light was pouring in from the left giving a nice back light effect.
This is straight out of the camera, RAW to Photoshop to JPG sRGB. RAW settings were all "as shot" and no adjustments made in the RAW converter. No adjustments of any type were added in PS. So as you can see, you can get some damn decent lighting right out of the can using an off camera flash bracket and bouncing the flash in a creative manner.