In short, your company will only need to offer vision coverage through COBRA if that coverage was also included in the original insurance plan. Because COBRA effectively operates as an extension of existing coverage, there aren't any additional regulations to offer new types of coverage once COBRA is used. An exception to this is if your company is going through open enrollment or adding a new line of coverage for the group, in which case the group must provide the same coverage options to COBRA enrollees.
Federal health care regulations don't require insurance providers to cover vision care for adults, so your company isn't obligated to offer vision coverage through either your standard health plan, or the COBRA extension of that plan.
Some states have additional regulations for COBRA coverage. Often referred to as "mini-COBRA," these regulations are generally used to require smaller companies to offer a version of COBRA coverage, even when they're not required to under Federal law. Typically, state laws make no special provisions for specific types of insurance, such as vision insurance. A simple internet search should be enough to find out whether your state has special provisions. For example, New York's Department of Financial Services
says that employers only need to provide COBRA coverage that is identical to the previously existing plan, which is not required to include vision coverage.
To summarize, federal regulations do not require you to add additional types of coverage to a COBRA insurance plan. State regulations may require you to offer COBRA to additional classes of employees but won't typically include provisions for anything but extending the existing plan's coverage.
COBRA FAQ - Get answers to frequently asked questions about Federal COBRA rules.
COBRA Rules by State - Find out whether your state has a "mini-COBRA" program or other changes from Federal regulations.
COBRA Coverage - Find out what COBRA covers.