Simple Present Tense may be used here - He tells me everyday that they are getting divorced. In this case 'they are getting divorced' means 'they will get divorced' in the near future.
Present Perfect Continuous Tense can also be used in the following way - He has been telling me for a long time that they are getting divorced.
Present Perfect Continuous Tense is used to describe an action which began at sometime in the past and is still continuing. So his action of telling me has began sometime in the past and he is telling me the same thing still now. So it is better to use Present Perfect Continuous Tense and also add a period of time (for a long time...) or a point of time (since three months...) to make it cent percent correct.