Use Consulate records for are located at the National Archives in College Park, Maryland. In the research room there, they have a large finding aide arranged alphabetically by name of Consulate. You would then need to look through the list of records from Karlsruhe for marriages or mixed records from the time period you are interested in. Once you receive the book(s) you would have to look through them for the marriage (most have no index and the records are usually arranged chronologically).
Dear Ms. Cannon,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the series Despatches from Diplomatic Officers, 1789 - 1906 in the General Records of the Department of State (Record Groups 59) and the series United States Consular Records for Karlsruhe, Germany, 1857 - 1874 in the (Record Group 84) that may contain marriage records for your great grandparents in 1873. For access to these files, please contact the National Archives at College Park - Textual Reference (RDT2) via email at email@example.com.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT2. We apologize for this inconvenience and appreciate your understanding and patience.
We hope this is helpful. Best of luck with your family research!