I'll be adding the lights I have to the coop this year, they are clearance solar outdoor holiday lights from two years back. Got them for <$10 per huge string, and used them last year to light up my porch for getting home (since it was always dark) and to let my dog be able to see when she hung out on the porch without having to use the porch lights (because my electric bills are crazy, oh the joys of whole house electric). One string will be plenty to do my 8'x16' divided coop.
Because of the shorter summer sun, as someone else mentioned, solar lights in the winter dim out in a few hours. Mine dimmed and eventually went off around 9pm in the winter (so about 4 hours of light to various degrees as it dimmed). In the summer they regularly stay on way later than I've ever stayed up due to the sun itself being out later and the total sunlight being larger, so I wouldn't use them in the summer (either disconnect the panel from the lights or cover it). Because of the gentle dimming before going out I don't think there will be any issue with a sudden loss of light.
As far as cost effective coop lighting without running a cord, I really think clearance solar holiday lights are the way to go based on how they preformed as porch lighting last year. If you have the time to plan a holiday season ahead and score some good clearance deals, that could save you a lot in the long run. (But less useful for those who need them this winter.)