Is there an abbreviation for the 黑海/地中海 combo?
I've never heard such a combination for (黑海/地中海).

Such combinations can be made up when needed. 中日 is used more often when may not need further explanation. 中 can be also combination with the initial character for other country names to form such combinations (like 中美), as long as you let the reader/listener know which country you're referring to. The full name of country should be already given in previous part of the article.

Other combinations of place names are also possible (like 北上广 for 北京 上海 广州), but not always acceptable.

These kind combination appears more in news articles. Some find their way into daily use, but most of them only appear in news.

NOTE: For Chinese city/province name, the abbreviation is not always the first character, like (沪 for 上海).