Indeed, using an arduino with a RTC (realtime clock) module would be your cheapest option (< 30 euro /dollar). Gives you more freedom as wel.
Just calculate the periods you want your device in terms of seconds since 1-1-1970 and have your code poll every minute orso whether such a period is begun. You do need to power the arduino of course. But maybe you can do that from the solar source?
a tut: http://www.ladyada.net/learn/breakoutplus/ds1307rtc.html
on to build your own
but you can also get these module preassembled http://www.sparkfun.com/products/99