Annihilationists use a lot of the same arguments as Universal Salvation supporters.

They will agree that references to a Judgment or Punishment itself do not prove endless punishment.  They'll likely agree with us on the Translation issues related to Olam, Aionios/Aionion and the Hell words.  They might also agree with me that the Fire of the Lake of Fire can be called Eternal because it's the Fire of God.  And they'll also seek to define their view of God as more merciful.

I can also agree with them that something will be Annihilated, that something is Sin.  And I agree with them that the Punishment for Sin that Jesus paid for us is Death, and that Salvation is The Bodily Resurrection from the Dead.

Many but perhaps not all tend to also support Soul Sleep.  The Issue of whether or not we actually have a conscious state between our bodily Death and The Resurrection I don't have a solid opinion on, I could go either way.

The Second Resurrection should be a logical problem for Annihilationism. If Salvation is being saved from death why bother resurrecting the unsaved just to immediately kill them again?  And Revelation 20 isn't our only witness to that, that Unbelievers will have a Resurrection is also in John 5, 1 Corinthians 15 and Daniel 12.  Paul also refers to it in Acts 24:15, and he was talking to Felix an Unbeliever, a Pagan Roman, and did not feel the need to tell him that unless you become a Christian your Resurrection will be useless.

Annihalationists will argue from John 5, Daniel 12 and the Sheeps and Goats Judgment of Matthew 25, that if the contrast is between Life and Judgment, the Judgment must be death since they don't have life.  And yet those texts still do not explicitly say that.

What they forget is the word "Life" is used of more then just the state of being physically alive, it can also be about Quality of Life.  People will talk about feeling more alive now then they ever had before.  Jesus message to Sardis talks about those who have the reputation (or Name) of being alive but are not.  In the context of Revelation 21-22 it could be about having direct access to the Tree of Life by being in New Jerusalem, as those chapters do clearly allude to the existence of people outside New Jerusalem, some of whom, at least at first, aren't allowed inside.

Annihilationists will also quote the same verse from Jude I like to quote about Sodom being destroyed by "Eternal" Fire, they will simply say Sodom was Destroyed.  But they are forgetting to account for Ezekiel 16 which promises that Sodom will be restored. 

A favorite passage of Annihilationists is Matthew 10:28 where Jesus says "fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell".  The proceeding context of this was Jesus saying if you fear anyone fear God.  God is able to Kill the Soul but that doesn't mean he will.

Once again what people need to do is read on.

"Are not two sparrows sold for a farthing? and one of them shall not fall on the ground without your Father.  But the very hairs of your head are all numbered.

 Fear ye not therefore, ye are of more value than many sparrows."

What Jesus goes on to say is not to Fear because God won't destroy us because He loves us.

Now I know people will respond with how Jesus goes on to talk about denying those who deny Him.  The point is Matthew 10 doesn't settle the issue.  Romans 5&11 settle the issue, as does what I already said about Revelation.

Also Soul and Spirit are not synonyms Biblically. Soul seems to refer to something animals also have while the Spirit is what's unique to Adamkind.  The Greek word translated Soul is Psyche.  It may be the Soul like the Body can experience a destruction before being Resurrected, "Hell" in Matthew 10:28 is Gehenna which refers to God's Judgment on the world at the end of time.

The Fire of God is for Purification and Purging according to Malachi 3.  God's Punishments are for Correction according to Habakkuk 1:12 and Proverbs 3:11.

In the Annihalitatiost view there is no need for Brimstone/Sulfer to be in the Lake of Fire, the fire is all that's needed to destroy.  Sulfer is used in the process of refining and purifying Gold, consistent with Malachi 3 and Proverbs 17:3 & 27:21.  Isaiah 30:33 says the breath of God is like Brimstone, just as God is called a Consuming Fire.

For more information read my post about The Baptism of Fire, and about Gehenna.

Revelation 20:10 is a bit of a problem for Annihilationism, a thousand years later and the Beast and False Prophet haven't been Annihilated yet, they're still there.

And I think the tears in Revelation 21:4 can be interpreted as tears of joy and happiness, not mourning people who were lost.