They should recharge at whichever dawn comes ~24 hours or more after the last time the stones recharged.
There are actually two answers to this, though obviously I prefer the above. One answer is by rules as written (RAW), and the other is by rules as intended (RAI):
RAW: They will recharge when either stone experiences dawn.
The exact time that dawn occurs depends on your location. It can be assumed that the location of the item determines when dawn is for that item. For most magic items, this is fairly easy to adjudicate, since there is only one dawn per day for any given location. Sending stones, however can be in multiple locations while still being one magic item.
The simplest interpretation is that the stones recharge twice, once when the first stone experiences dawn, and then again when the second stone experiences dawn. This could be seconds apart, or minutes, or hours.
RAI: They recharge every ~24 hours.
Looking at designer intent, nearly every single magic item recharges at an interval of 24 hours, whether it's dawn, dusk, midnight, etc. Most likely, the designers didn't anticipate any of the complexities that come from a strict interpretation of "dawn" and such, but rather meant it as just a bit of flavor to make magic items seem cooler. They could just as easily have said that all of them recharge when you finish a long rest, but that breaks immersion and is less mystical.
To support this, imagine what would happen if a strict definition of "recharge at dawn" was taken. Any magic items that recharge at dawn could, in theory, be recharged multiple times per day, if the user is atop a hill or mountain. Simply let the item recharge when the sun hits the top of the mountain, use it, and then race down the mountain to a point that has yet to be reached by the sun. When the sun dawns upon that location, the item recharges, and can be used again. Race further down the mountain, and repeat until you run out of dawns to recharge your item with.
Even without a mountain, if you can move faster than the earth revolves. At or near the equator, this would require absurd speeds, however near the poles dawn "travels" slowly, approaching zero speed, and anyone could recharge their items over and over again by simply walking ahead of "dawn".
Since such a situation would be absurd, a restriction needs to be put in place to prevent such exploits. Given that the developer's assumption seems to be that dawn will only happen every 24 hours, then the logical way to limit this is to have magic items recharge only if the condition is met, and ~24 hours have passed.