Of course that you can deny that evil exists and some people do.
To most of us, the existence of evil appears to be undeniable. There is widespread suffering in the world. We have all experienced some amount of pain, both physical and emotional; evil confronts us all. Some, however, have sought to deny the reality of evil, and so to eliminate the problem of explaining how evil can exist in a world governed by God.
Christian Scientists are among those that teach that evil is an illusion. The movement’s founder, Mary Baker Eddy, wrote, “Sin, disease, whatever seems real to material sense, is unreal.” Suffering, on this view, may appear to surround us, but this only an appearance.
It is difficult, however, to dismiss all evil as illusory. If it appears to me that I am racked with disease, but that appearance is merely illusory, then it is nevertheless a painful illusion. Even if the disease is no evil because it does not exist, the appearance of disease remains an evil. Objective suffering may, perhaps, coherently be dismissed as illusory, but subjective suffering cannot be.
Far more promising than the dismissal of evil as illusory is the Augustinian and Thomist view that it is nothing more than a privation of good. According to this view, evil is not a positive thing that is out there in the world, but merely an absence of good.
God therefore cannot be blamed for bringing evil into existence; evil is not a thing and so was not brought into existence. The idea that the world contains evil (i.e. certain privations of good) can thus be reconciled with the idea that it was created by a God who would not create evil; it is only the good in the world that was created, the bad is merely an absence of good.
Even if this account of evil were accepted, however, it would not completely resolve the problem of evil. For it may still be asked why God neglected to create those goods that are found to be lacking in the world. Even if evil is simply an absence of good, there is a tension between this absence of good and the existence of a Creator that knows how to, is able to, and wants to create all goods. The problem of evil, then, in some form at least persists.
