The conure group of parrots includes several different varieties of bird, including the sun, jenday, nanday and Patagonian conures. The sun conure is probably the most common pet conure, and is certainly the most recognizable of the conures. In general, conures are not good talkers, but there are a few exceptions. Most conures have a gravelly voice, making them hard to understand. The larger conures, such as the cherry head, blue crown and the Patagonian, are more likely to talk than other conures.
Repeating a word or phase to a parrot three or four times every time you interact will increase the likelihood that the bird will pick it up. Of course, this is not a guarantee. Parrots as very smart and have a will of their own. A bird will only learn the words it wants to. Sometimes, after weeks of saying a phrase to no avail, an owner will move on to the next word and the parrot will pick it up in one sitting.
It is important to make training a fun time. Just like children, parrots learn best when they are engaged in the activity and having fun. Make sure that the tone of your voice stays upbeat and energetic. Conures are flock animals, and they love to play and please their flock leader, which should be you. If you don't sound like you are enjoying the game, they will not be interested in it.
Training conures is similar to training other animals, such as dogs. Positive reinforcement goes a long way. If you are walking by the cage and your conure says a word, stop and engage the bird or take it out and play for a minute. When training, reward the bird with treats or head scratches for a job well done.
It should be noted that conures are notorious for their screaming. Teaching your conure to talk and rewarding the bird with playtime for talking rather than screaming will help curb the screaming somewhat. However, screaming is a natural behavior and it will happen whenever the bird gets excited, scared or lonely. Before purchasing a conure, be sure that their screaming is something that you can tolerate.