Do you have a datasheet/part number for the LEDs, or at least a picture and diameter?

Because battery voltage reduces over time, the LEDs will get dimmer as the battery drains fairly quickly. If possible, running it off a mains plugpack (e.g.12V like for a router or external hard drive) would be good.

An example UV LED has a forward voltage of nominally 3.7V. Two in series on a 12 (8x1.5V) supply gives us 12V-(2x3.7V) =4.6V to drop across the resistor. We want ~15mA, so need a very roughly (V/I =R) 4.6V/0.015A=300 ohm resistor.

When the battery is nearly discharged, at 1.1V/cell it will be 8.8V, giving 1.4V across the resistor and V/R=I 1.4V/300ohm= 4.7mA.

So you would connect each pair of LEDs as:

BAT+ RES +LED- +LED- -BAT all in series. Like this.