Can someone give a verbal acceptance to COBRA within the required timeframe and then followup with the paperwork?

There's nothing in the regs that says this isn't permissable, so if you do allow it, I would recommend following up with a memo regarding the conversation including date and time so you can start the 45 day countdown for the first month's premium. Furthermore, I would only allow this if the employee had a pretty damn good excuse, i.e. was in a coma, was kidnapped in Columbia.... 60 days is plenty of time to decide what you want to do.

There have been several court decisions related to this, some going one way, some going another, but the consensus is that oral elections are allowed. It is srongly recommended, however, that this question be addressed in your plan doc as well as on your COBRA offer letter. Even though oral elections can be allowed, you are under no legal constraints to allow them if your plan doc and offer letter specifically require written agreements.