The idea falls apart pretty quickly when you consider the capacity of batteries that size and the number of LEDs you'd need to light up each dot (assuming individual LEDs for each dot).
Mexican Train is played with dominos having up to 12 (16?) dots on each end - a maximum of 24 (32?) per domino. The dots are also colored: black, red, green, yellow, blue and pink. Since you can't get black LEDs, you might replace those with white LEDs. The white, blue and pink LEDs will have a high forward voltage, probably even greater than a 3 volt lithium cell can provide.
Ignoring the voltage issue for a moment, a **broken link removed** is designed to power a 1500 ohm load - less than 1mA. Not much chance of powering 32 LEDs with any brightness for any length of time. A better option might be a 3-volt 2016 or 2032 lithium cell. These can provide 15mA
for short periods of time. And you'll probably need 2 per domino to get enough voltage to operate the white, blue and pink LEDs. Looks like you can get 2032 cells for about a buck a piece...x 91 dominos x 2 = $$$.
Something a
little more practical to use material like **broken link removed**. This material is clear on the top with a thin laser-engravable color layer on the bottom. In
this article, I show how the material can be laser-engraved to let an LED shine through the desired areas. Engrave the dot patterns for each domino, and put a single LED behind each end to illuminate the dots. You'd still need a butt-ton of batteries but at least they'd last longer...and all the dominos would have about the same battery life since each battery is powering just 2 LEDs.