Random Battles
The amount of time it takes for your Chocobo to breed again is based on a randomly generated number of random encounters, so the best thing to do while waiting is to participate in random battles. The cooldown time for an adult Chocobo is anywhere between 3 and 10 random battles, while the cooldown or maturity time for a newborn Chocobo is between 3 and 18 battles.
Explore
"Final Fantasy VII" has a number of side quests that must be completed in order to obtain each character's strongest weapon, strongest limit break and the game's strongest Materia. While waiting to your Chocobo to cool down, explore the world map and search for some of these side quests. You will invariably run into some random encounters along the way that will contribute to your Chocobo's cooldown time.
Chocobo Races
One of the factors that goes into successfully breeding a Chocobo is the combined number of race wins its parents have at Gold Saucer. Navigate your Chocobo or the Highwind ship containing a Chocobo to Gold Saucer, just south of North Corel. Speak to Ester once you are at Gold Saucer to enter your Chocobo in a race. Along the way, be sure to get into some random encounters to ensure your Chocobo will be ready to breed when you return.
Continue Story
If you still have some of the game's main story to complete, you can continue on to your next destination while you are waiting for your Chocobo to cool down. As you complete the game's story mode, you will engage in a number of battles that will count toward your Chocobo's cooldown so when you are finished with the story quest, you can return to the ranch and breed the Chocobo.