One of Mexico's premier birding locations is Volcan de Nieve, the "Snow" Volcano. A decent rock road winds up through various habitats until reaching 12,300 feet. There a gate blocks additional ascent but you can walk farther up until finally rounding a curve and, if there are no clouds, seeing a breathtaking view of steaming Volcan de Fuego, the "Fire" Volcano, about four miles away. Near the top, there is a gate where the park charges 20 pesos to continue.
It is futile to try to list birds here - the number of species possible probably runs into the hundreds, and ranges from Blue Mockingbird at the base to Red Warbler, Cinnamon-bellied Flowerpiercer, and Chestnut-sided Shrike-Vireo on the way up to Red Crossbill and Yellow-eyed Junco at the top. Some of the specialities to be found here with some effort include Long-tailed Wood Partridge, Crested Guan, and Singing Quail. You should be able to find Gray Silky-Flycatchers along the way. Look on-line for trip reports and bird lists for a more complete accounting.
The turn-off to the volcano is at Ciudad Guzman, about 50 miles north of Colima on the highway to Guadalajara. Turn right into town, and watch for the road going right, Libramiento Pereferico del Sur, which takes you to the free road to Colima. Take this road past a wide curve to the left to Reforma and follow to the highway to Colima. Keeping right at forks, you will pass the Technological Institute and prison. Watch for the Volcano National Park sign on the left.
Another important area birding spot is Laguna Zapotlan just north of town. To get there, return through Cd. Guzman the way you entered, except continue on straight through the traffic circle and past the city entrance road. You will soon come to the huge natural lagoon that is always worth checking for ducks, herons, shorebirds, and gulls and terns. Since this is a busy and narrow highway, parking by some appealing areas is difficult or dangerous. One safe parking area is the marina where the road turns sharply right; you won't be allowed to go left. The marina offers an excellent view of much of the lagoon and often has interesting birds nearby. To continue your trip around the lagoon, take the sharp right, go about .2 miles, and go left on the highway, resisting the temptation to try to get to the lagoon on your left by driving down one of the dirt roads. Instead, continue on to a hard surface road that goes back sharply to the left and across an edge of the lagoon. This road offers excellent viewing of both lagoon and marsh habitats and even has elevated observation towers. You may have to drive slowly to give the Great and Snowy Egrets time to get out of the way. This and nearby marshes are a primary wintering area for Yellow-headed Blackbirds. One of the great spectacles here is the early morning and evening clouds of them heading out to feed and then returning.
Since birding the volcano and Laguna Zapotlan can take a full day, it's probably best to plan an overnight stay. I have little recent experience with lodging there but did notice there are at least two decent looking hotels along Libramiento Pereferico del Sur. If coming into town they're on the right side and before the wide curve. This location offers good access to both the volcano and the lagoon. If you can't manage an overnight stay and want to do a long day trip, remember that driving at night in Mexico is never recommended so plan for daylight driving.