We had co-signed a rental agreement for my son, they have defaulted on the last 2 months of their lease. Now the landlady has written to us stated that this problem and has not taken eviction notice but will. We want out of the co-sign how can the kids get get out of the house, what happens with eviction?

You don't 'get out of' a lease or any other contract. You are liable for whatever you signed for or co-signed for, and can be sued for what is owed all the way to the end of the lease, even if they leave.
The part about defaulting on the 'last 2 months of the lease' sounds like the lease has ended, yet you are asking about eviction, so do you mean that they haven't paid for the most recent 2 months?

Eviction procedures depend on where you live. Use Answer below if you want people here to look online for you. In general terms it involves written notice, court filing, and eventually a sheriff or constable physically removing the tenants.

When you say your son defaulted on the last 2 months. Does that mean he is still living there? Or did he vacate. If he is living there you are responsible for the rent. That's what being a co-signer means. There is NO way to get out of that. However, if he vacated, then you are just responsible for the balance of the lease. The landlord doesn't have to evict, just sue both your son AND you for the balance. Plus, if she re-let the apt before the expiration date of the lease, she can only sue for the time of vacancy.

However, if he is still living there, then she will have to file for an eviction, then sue him and you for any unpaid rental until she re-lets or the lease expires, whichever comes first. You also need to inform her, in writing that you will not be co-signing any lease renewal or extension.

Another good reason to not co-sign a lease for ANYONE unless you are confident of them paying the entire amount.

You will be liable for costs for as long as he is still living there, since you signed to be liable for it.

So if he is not going to pay, and he is already in default ( from what you said) he needs to move out and then you pay for any and all of the rent that is due,
Or just pay for it now to settle with the landlord.