When most people buy red-eyes in the store, they probably never think about breeding them, but they are not that hard of a frog to breed, if you have patience and the right setup.
First, you want to read all you can on tadpole propagation and care. Once you feel you have enough knowledge on keeping tadpole's, you are now ready to start a breeding program for your frogs. red-eyes have a better chance of producing eggs if you give the females a choice of males. Almost all of the people I have talked with except one, has told me that you need a minimum of 2-3 adult males for every adult female you want to breed. The reason being that when the males are ready to breed, they will call(chirp), and another male will return the call, but a little bit higher in pitch than the previous call, and usually a bit louder(to show that he his bigger and "toughest" than the previous frog), this can go on for hours at a time. Sometimes, one backs down and the winning male will be allowed by the female to mount.
To get the frogs ready for breeding, you have to simulate the seasons of their native homeland(mostly Costa Rica). Costa Rica has a dry season and a wet season, the dry comes before the wet season. To simulate the dry season, You need to keep the cage cooler(70 to 75 during the day and 65 to 70 during the night), you also need to cut down on misting the cage, but make sure there is some moisture in the cage, if you have a small waterfall setup in there, you wont have to mist at all during the dry season. With the cooler temperatures, the frogs metabolic rate will slow down and will require less amounts of food and less attention, but you should still check on your frogs every day to see that they are still ok and have not encountered any problems such as cuts or scrapes. The photo period should be shorter too, mabey 8 hours of light and 16 hours of darkness. Keep this up for about 6-8 weeks and then slowly make the photo period longer, mabey by 20 min every 3 days till you get back to 12 hours of light and 12 hours of darkness. With more light, the cage should warm up to about 75 to 80 degrees, with the longer photo period and the warmer temperatures taken care of, you are now ready to start the rains of the rainy season. You should start to feed your frogs more and powder their food with a vitamin supplement.
If you have an automatic misting system, then this will be a piece of cake, if you dont, its going to take some time each day to mist down the cage 3-4 times a day. Now the males should begin calling at night, you should watch them to find out who your dominant male of your group is, usually its the biggest and loudest of the bunch. You can now keep the frogs in the same tank and watch for them to get into amplexus, or you can remove them and put them in a breeding tank. The breeding tank should be set up like this: A tall aquarium, filled with about 5 inches of gravel and about 4 inches of water. You should put some type of filter system in there to keep the water from getting stagnant and to keep it clean. With a filter in place, you can set up the out take of the pump up to make it "rain" in the tank by using a spray bar thats usually used for canister filters. You dont want the water to be spraying out of that tube, a slow trickle is all you need. Place a couple of wide leafed plants in the gravel. Place some bark slabs in the tank as well as some more plants. The lid should not be solid, it should allow some air to pass in and out of the tank. No artificial light source or heat source should be used at this time, if the tank is near a window, use a white sheet to shield it from some of the brightness and heat of the sun. With this setup, you should have no problem collecting eggs from your frogs throughout the rainy season.
When your frogs are in amplexus(picture), dont be alarmed if they stay that way for a couple of days and dont produce any eggs, sometimes it takes awhile. The first time my frogs went into amplexus, the male was attached for 2 days before I got worried and separated them, which was a big mistake on my part, none of my frogs were harmed, but I did not get any eggs that time. Check the sides of the terraria and the plants every morning for egg masses. When you feel that you have enough eggs, I would separate your males and females to let them recoup from the strenuous activity of breeding. If you find any egg masses on the walls of the cage, use a spatula and carefully remove them from the walls of the cages and place them on a clean, cut broad leaf, if they are attached to a leaf, just cut the leaf and place them into a incubation jar. The incubation jar is a one gallon jar with about 2 inches of water in it with a sponge filter running, the leaf should be placed diagonally in the jar, not allowing the mass to touch the water, with in a few days the egg mass should start to dissolve and little black tadpoles should wriggle their way into the water. You should limit the about of tadpoles to about 9 to 10 a jar to prevent overcrowding and cannabilsm. Tadpoles are alot like fish, so rear them just as you would baby fish. They are omnivorous so feed them flake food for omnivorous fish. The amount of time it takes tadpoles to metamorphosis depends on temperature, the warmer the temp, the quicker they metamorphosis. Dont think that if you make the water temp 90 degrees that they will hop out of the water in a few days, no, it does not work that way. Water temperature should be about 78-80 degrees. When their front legs begin to develop, remove them from the jars and place them into a 10 gallon take set up with a wet/dry environment, meaning that there is dry land for them to crawl out on if they need to. The water in the 10 gallon should be aerated and filtered just as a normal fish tank would be. Be super cautious on the amount of Ammonia(NH3) in the tank, it is one of the major killers of tadpoles. You could take some pieces of cork bark and float that on the water too. They will climb out on to the land and sit still for a few days till their tails absorbed. Once their tail is gone, carefully remove them and place them in your original frog tank. Have the approiate size of food ready for them, dust the food with vitamin supplements that contain Calcium and Vitamin D3. with in a few months you should have healthy juveniles ready to sell or you may just decide to let them mature, which takes a minimum of one year and start them breeding. Remember, frogs that interbreed and breed too often, do not live very long. So space out your breeding cycles and it might be wise to separate the kin from the parents when you are ready to breed again.