I am going to try to minimize block quotes in this answer.
Your question is problematic for two reasons. First, I think this really depends on how you define "long term." Also, no matter what anybody says there will always be somebody who predicts the opposite, and can claim to have been correct. I will try to address what was the consensus at the given time.
If we are talking about 40-50 years ago, there have been few real successes. In fact, in the 1970s people believed in "global cooling," that we would soon see massive glaciation across the entire world. This culminated with the plan to cover much of the world's deserts with oil, to soak up heat and prevent the global cooling. Fortunately, this plan was never enacted.
On the other hand, if you consider acid rain to be a climate issue, we have been remarkably successful in our predictions of this, although we did overestimate how bad the issue was. Acid rain never was as harmful as many believed. I guess that our almost-elimination of acid rain could be considered a triumph of long term climate predicution.
Another long-term climate prediction was the depletion of the ozone layer. Our predictions on this front have been pretty bad. In the 1980s we predicted a decrease in ozone of 7% over a 60 year period. Today this has been decreased to 4%. We also missed dramatically in our belief that ozone holes would pop up all over the globe. To date there are only two such holes.
I couldn't really think of anything else to investigate. But, there you go.