How do you call "pocoya" bird in English?
I have done some reading based on your descriptors of the bird and your examples, the bird in question is a nightjar and I think they are referring to the Common Paruaque. All nightjars fit your first 2 points, the 3rd point is the only clue we can use to determine what species of nightjar you are describing. There are 11 species of nightjar is Nicaragua.

It seems the Common Pauraque (Nyctidromus albicollis) is commonly known as the "Pocoyo" in spanish, but the spelling may not been certain. Here's a quote from page 9 of an article on the birds of Nicaragua from 1957:

"The species is known in Nicaragua as “Pocoyo” (exact spelling uncertain)".
Reference.

The other bird you describe, the Ocellated Poorwill (Nyctiphrynus ocellatus) is referred to as the "Pocoyo ocelado".

The only other nightjar that might be called Pocoya is the Common Nighthawk (Chordeiles minor), but it is referred to as "Anapero".

I believe when referring to "Pocoya" it is most likely the Common Pauraque as the Ocellated Poorwill would have another descriptive word in it's name in spanish.