What's the application of this circuit? My gut feeling is that you've not got enough power there to drive 8 LEDs for a significant period of time. You're looking at around 50 to 200 mAh for a watch battery.
It will be inside a wood/acrylic drink coaster. Not a ton of room, I could cut it down to 4 leds if I need to. Any suggestions on batteries? I can fit 4 watch sized batteries or maybe fewer larger batteries.
I was just trying to see how much light you were after and for what duration. A spec sheet I've just looked up for a typical LED says about 60mW. 4 watch batteries, 3v, 200mA, is 2400mWh. So you could be looking at powering 8 LEDs for 5h. However, most watch batteries are intended for long duration applications (eg, a watch!) so I don't know what their characteristics would be like discharging comparatively high currents over a short period of time.