The most rabid Zionist supporters are evangelicals, so the best way to counter them is to actually teach them the Bible. Most evangelicals are cults of personality with Bible flavoring and preach utter heresy–dual covenant theology and Zionism, for starters. The following are the best arguments for debating and trumping zionist evangelicals:
Behold, I will make them of the synagogue of Satan, which say they are Jews, and are not, but do lie; behold, I will make them to come and worship before thy feet, and to know that I have loved thee.
– Revelation 3:9
This points out how the Jews, as they call themselves, are not Godly, and that their subversion was predicted.
And if ye be Christ’s, then are ye Abraham’s seed, and heirs according to the promise.
– Galatians 3:29
This destroys any notion of a Jewish right to the land of Israel based on the Bible, as the chosen people are those that accept Christ as savior–not a particular race and certainly not those that rejected Him.
Whosoever denieth the Son, the same hath not the Father: (but) he that acknowledgeth the Son hath the Father also.
– 1 John 2:23
This destroys the idea that the Jews are still the chosen people, because they have denied Christ and so have denied God.
Then said Jesus to those Jews which believed on him, If ye continue in my word, then are ye my disciples indeed; And ye shall know the truth, and the truth shall make you free. They answered him, We be Abraham’s seed, and were never in bondage to any man: how sayest thou, Ye shall be made free?
Jesus answered them, Verily, verily, I say unto you, Whosoever committeth sin is the servant of sin. And the servant abideth not in the house for ever: but the Son abideth ever. If the Son therefore shall make you free, ye shall be free indeed. I know that ye are Abraham’s seed; but ye seek to kill me, because my word hath no place in you. I speak that which I have seen with my Father: and ye do that which ye have seen with your father.
They answered and said unto him, Abraham is our father. Jesus saith unto them, If ye were Abraham’s children, ye would do the works of Abraham. But now ye seek to kill me, a man that hath told you the truth, which I have heard of God: this did not Abraham. Ye do the deeds of your father. Then said they to him, We be not born of fornication; we have one Father, even God.
Jesus said unto them, If God were your Father, ye would love me: for I proceeded forth and came from God; neither came I of myself, but he sent me. Why do ye not understand my speech? even because ye cannot hear my word. Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it. And because I tell you the truth, ye believe me not. Which of you convinceth me of sin? And if I say the truth, why do ye not believe me? He that is of God heareth God's words: ye therefore hear them not, because ye are not of God.
– John 8:31-47
Taken together, I have taught these passages to several tea party and conservative groups to massively undermine their support of Israel. You will be attacked at first, but if you learn the passages well enough, you can stump them and change the whole group.