When you buy a pre-existing home, you may have the option of purchasing a home warranty. This is a special type of home insurance which covers such things as your hot water heater, built-in appliances, and your air conditioning. However, a home warranty is different from your homeowners insurance, and it is important that the two are not confused.
Homeowners insurance protects you against the perils named in the policy, such as wind damage, fire, water damage, tornadoes, civil unrest, etc. Unless your central AC unit is damaged by one of those perils, then you will not be able to use your home insurance to pay for repair or replacement. If your AC is damaged as a result of a covered item, such as one of your trees falling on the unit, then you are protected and should contact your insurance company to arrange for an adjuster to visit, or contact a few contractors to start compiling a list of estimates to base your insurance claim on.
Another way to cover your central air unit would be to purchase a separate maintenance contract. Such contracts will usually include regular maintenance such as checking the coolant, cleaning the ducts, or replacing filters, and will pay for all or a specified portion of the repairs if your AC unit stops functioning. This is not an insurance plan, but is a contract you engage with a licensed air conditioning contractor to prolong the life of your air conditioning equipment.