We have always used the combined counteroffer - adverse action letter allowed by §202.9(a)(1)6 of the Regulation B Commentary.

We are considering sending separate notices and I was looking for an example of a counteroffer letter without the adverse action section. Does anyone know where I might find an example?

I am not aware of a separate notice that does not have a section for the denial also. You could probably just create one on your institution's letterhead.

I replied because I would like to caution you that if you go with separate notices and the customer does not accept the counteroffer, you must still send the denial (of the original application) within "90 days after notifying the applicant of a counteroffer if the applicant does not expressly accept or use the credit offered." (FDIC Pg7218). We were written up last time on this, so I know from experience. We just use the combination form as standard practice to avoid violations.