I don't think any 'real' scientists deny existence of black holes. It is mathematically/physically understandable and working concept (Einstein's theory of relativity). And so scientists knew it before they saw any of them. Usually the scientific discussion is already on the nature of the black holes (like do you loose information what they swallow).
Because black hole sucks everything including light, it cannot be seen directly (well it is just a black circle). But you can 'see' it indirectly in few ways...
1) A star (in binary systems) is orbiting it. It can be calculated from this how much mass the BH has.
2) Something is being sucked into it. This is usually like hot gass which while being heated generates EM radiation not just in visible length.
3) Gravitational lensing. Mass makes space to curve and light follows this too. So large mass makes light bend. BH and even less massive objects like Sun bend light from background objects (other stars).
...maybe something else too I cannot remember right now... All of these have been spotted and verified.
If it is hard to understand the concept, you might try to think it just as an object which has escape velocity over the speed of light (=c) (the surface where it is exactly c is called event horizon and no information can be get from inside, where ev>c).
Also the objects closest to density of BHs, the neutron stars, bend light a lot. Because we know that more massive stars: a) exists b) in death collapse into something more dense which has escape velocity>c. ...then do you need more? It is not even the hardest concept. Try understand that universum is not infinite, but is still infinite (where does it expand? from what did it originate? etc), but you still do not deny it's existence, right?
It is thought that there are lot of 'loose' black holes wondering around. If they are not feeding, and they have no visible companions, the only way to see them is gravitational lensing. It took some long time and careful observation of space, before they spotted it. Some large black blob moved over some background stars and the light from them is bended. This gave me real 'goose pimples' when I saw the clip. It was really convinsing - this could mean that our solar system might meet such a thing too and we could do nothing. Maybe we wouldn't even notice it until the orbits of outer planets started to go funny. An 'interesting' way to die