An all-evil deity wouldn't allow good to exist. If God is all powerful, then he is able to remove all the good. If God is all evil, then he would want to remove all good. Why is there therefore any good in the world if such a deity existed. At most this deity is either impotent or not all-evil... you'll need to settle for a less powerful deity or a little less evil one.
Counterargument: All good in the world is really an attempt to jerk us around and achieve a greater evil. If it was all evil all the time, how would we know how bad we were being screwed over.
Rebuttal: If God were truly all powerful he could achieve this evil without needing to use good to do it.
Counterargument: Good is the result of free will. God is so evil that he trusts a bunch of stupid apes to make their own choices in order to not only have evil result but make it actually their fault. As such, good is just a unintended side effect of free will.
Rebuttal: There are many good things which happen which have nothing to do with free will. For example on Friday the 13th in 2036 an asteroid called Apophis will narrowly miss Earth. This is good, however it isn't good because somebody messed up, nobody's free will played any part in this. In short, ignoring free will... the world could be worse.
Counterargument: This world is minor and temporary. Regardless of what passing good might but in the long run it is moot because you are going to burn forever and ever and ever in hell regardless of what you do. Though, if you do do too much good God may send you to Heaven, this isn't because he's good but because that's what you earned. This in no way implies that God is anything but pure evil.
Rebuttal: Giving a person a life in paradise to live peacefully is the antithesis of omnimalevolence!