The cost depends upon the contract that the airline has signed with the service provider e.g. ARINC, SITA...
Normally there is a certain number of kilobytes of traffic included with each aircraft that is registered to use ACARS but then there is an extra charge for any overages of that limit. Normally most airlines sign a contract with a primary service provider and then have contacts with secondary providers. The cost of an ACARs message on the secondary providers can be 5 to 10 times the cost of the same message on the primary provider.