Is there a universal label for the sustainability impact of a specific coffee product? I am interested in the environmental impact of coffee and am therefore wondering whether a system exists for labeling the environmental impact of coffee. So not so much brands, such as Fairtrade, but rather if it is possible for the consumer to get information about how sustainable the plantation associated with the specific coffee product (beans, grounds or powder) is, and if there is a scale to measure it?
There is no universal label though there are various labels for coffee sustainability.

You can't really have an universal label as each of the labels have their own standards which have to be met and various coffee farms and producers follow certain ones. For example, in the Huffington Post, it mentions some of these labels:


USADA (or simply USDA): This is basically the United States' label for organic for various products (i.e meat and fruits) that is not limited to only coffee. It is quite strict (has certification agencies, checks for criterion not only during production but also distribution and packaging) as it


  Aims to promote and enhance natural soil activity and cycling of resources, which helps to create a rich and fertile substrate for the crop and maintain ecological balance by prohibiting use of artificially produced (synthetic) agrochemicals.

As mentioned by @avacado1, there is an European equivalent to the USDA, which is the EU Organic Program (note that the EU doesn't cover all of Europe). Source
Some companies like Starbucks have their own labels that guarantee their standards for their coffee:


  C.A.F.E. (which stands for Coffee and Farmer Equity) evaluates the economic, social, and environmental aspects of coffee production in order to ensure that Starbucks’s sources of coffee are sustainably grown. Starbucks collaborated with Scientific Certification Systems (SCS), a third-party evaluation and certification firm, to develop the guidelines for the program.

Rainforest Alliance Program: This is a more "natural" certification since:


  With this program, coffee is grown on farms where forests, rivers, soils, and wildlife are conserved and workers are treated with respect, paid decent wages, have proper and safe equipment, and are given access to education and medical care.

Bird Friendly Conversation: This label ensures that the coffee farms support the native and migratory birds that come over for a visit:


  The Smithsonian Migratory Bird Center (SMBC) gives this certification to farmers in order to promote shade-grown organic coffee plantations that can play a key role in the conservation of our global environment and of migratory birds that find sanctuary in these forest-like plantations.





So as you can see here, the various labels not only have various standards and goals but have their own area jurisdiction as well, each trying to gain support based on what they are.