There are 3 ways and only 3 ways your finance could legally claim your son on a future tax return.
1. Get married and file a joint return. This is a bad idea because your combined income will be so high that you 2 together will actually get a smaller joint refund than if you remain single & get 2 separate refunds. Welcome to the marriage penalty.
2. Fiance adopts the boy prior to 12/31/2007. Now the kid is his son. Under current law, fiance could then claim the boy as a dependent even over your objections. On the other hand, you can sue for child support if you leave the guy whether you ever marry him or not. Conversely, he can sue for custody and/or visitation. Also, if the adoption happens prior to any marriage, the fiance could claim an adoption credit. Adopting a stepchild cannot give rise to an adoption credit.
3. Go to court & have the boy "placed" with your fiance as a fosterparent. Fiance could claim the boy on his 2008 return, but not on his 2007 return. (Placement has to occur prior to June 30 under your circumstances.)
Note that none of these will let him claim the boy on a past return.
BTW, I agree that you should think long & hard about marrying this guy. He is being selfish & manipulative, threatening you if you don't help him commit tax fraud. Sure, he'd save 2-3 thou$and, but you'll pay at least $1,800, so the net household savings isn't worth the drama he's creating. These are not minor character flaws; jealousy & manipulation & threatening to withdraw support if you don't back down are red flags that should send you running for the hills. Or at least make you insist on some intensive therapy for him & yourself. (Him to address the alarming behaviours; you to figure out why you are willing to tolerate it. Do you really want your son to grow up to be just like him?)
The fact that his accountant has given him bad advice is irrelevant -- I suspect he's either edited what he told the accountant or is hearing only what he wants to hear. Certainly the things this forum has mentioned should have been sufficient to alert him to give his accountant a little more info. You might try contacting the accountant directly & explaining all the facts & asking how the accountant thinks they can get around the qualifying child problem to let this guy claim the kid. You'd at least know whether the accountant is giving bad advice or operating under wrong information.