Notice that I'm not talking here about the actual existence of something, but the possibility of existence.
About such ways, I only know one that is argumentative (which is the kind I would like to have as answer), which is to point out that the thing in question exists (if it exists, then it's the case it's possible for it to exists) and one personal (that is to say, one can use for himself but not in an argument), which is the union of
- not seeing any explicit contradiction in the concept in question,
- having no reason to think there is a implicit contradiction in the concept and
- having no known reason to think there is something in the actual world that would make the existence of that thing impossible
. What other methods apart from this two exists? (specially that are valid for arguing (in an argument) that it's possible for something to exist)