Step 1: Understanding the process.
During anaerobic respiration in \textit{Methanococcus}, carbon dioxide is the terminal electron acceptor. This organism uses carbon dioxide as the final electron acceptor in its anaerobic respiration process.
Step 2: Analyzing the options.
- (A) Incorrect, nitrate ion is used by other organisms, such as \textit{E. coli}, but not in \textit{Methanococcus}.
- (B) Incorrect, sulfate ion is used by some bacteria but not in \textit{Methanococcus}.
- (C) Correct, \textit{Methanococcus} uses carbon dioxide as the electron acceptor.
- (D) Incorrect, oxygen is used in aerobic respiration, not anaerobic respiration in \textit{Methanococcus}.
Step 3: Conclusion.
The correct answer is (C) Carbon dioxide.