There have been many comments on this Instructable regarding DC vs AC solenoids.
I am using Rainwater 24V AC Solenoids - and they operate well using 12V DC.
Essentially, when operating a solenoid outside it's design specification, you have to understand that your experience may vary, depending on the manufacturer.
As one posted indicated, the inductance of the coil is what limits the current flowing through the solenoid to a safe value when driven in an AC circuit. In a DC circuit, there is no inductance, just the resistance of the coil. I would never recommend operating a 24V AC coil at 24V DC, that will certainly overheat the wiring, leading to premature failure.
One commenter did mention that using a coil with DC will increase the amount of heat that it had to dissipate - This is correct, as long as you don't reduce the supply voltage. Depending on the DC resistance of the coil, you may find that your specific coils run just fine.
My advice, use a 12V battery, and a multimeter measuring current, and see whether (a) the coil is pulled in enough to run, and (b) how much current is flowing when the coil is energized. As long as there is less than about half an amp, then you are likely to have no problems.
I am working on a 24V AC version of this design, so that peoples concerns are alleviated - but that won't run using a solar cell as it needs an AC supply to operate.