For monochrome OLEDs, the Arduino does not need to transfer too much data.
So 3 to 15 FPS should be possible with U8glib (depends on the display content):http://www.newhavendisplay.com/nhd2712864ucy3-p-3621.html
EA offers displays for different environment conditions.http://www.lcd-module.com/eng/pdf/grafik/dogm128e.pdf
For bright light conditions you probabaly want a display which is readable without backlight: DOGM128L or DOGM128W.
Backlight LED is sold as an option for the DOGM128, it can be replaced if damaged
i think the trick is, not to use the backlight LED at all, but let the sun do the lightning work for you.
Both displays are supported by U8glib (http://code.google.com/p/u8glib/