Hiking and camping.
In general, Panamá has not developed the custom of camping, as you would use the term elsewhere.
In Panamá, the term "camping" is actually used for what children do during times of vacation, from 1 to 3 weeks, when they usually go to some of the towns with proper installations, mainly churches or schools. "Camping parks", or large places where people can get together and do this, don't exist in Panamá, like they do in other countries.
But, on the other hand, Panamá is a great place for hiking and camping, in a different way, especially because the beautiful weather all year round and warm people who welcome you everywhere you go, even if they do not speak your language, but they try to communicate with you somehow.
Specifically around Coronado, you can find uncounted hills, mountains, rivers and paths where you can have an unforgettable experience. Two places in the area suitable for both activities are El Valle de Antón and Campana Hights. But you´ll have to provide all the equipment needed, unless you hire an outdoor adventure tour operator, who helps you with these items. You can also contact "ANAM", which is the government institution in charge of all the natural environment. They offer guidance on certain packages and tours, at excellent prices... like the park in Campana, or (8 hours away from Panama City by car) Cerro Volcán , in Chiriquí Province.