If a king dies in Adar and his son is not installed until Nisan we date the first year only for the first king and the second king only for the second year. This would imply that there is certainly a lag between the 2 events. How would documents be dated from the beginning of Nisan until the new king is installed (e.g. he is installed on the twentieth of Nisan)? We cannot use the first king (he is no longer alive and thus will never have had that number year in his reign). The gemara says that we cannot use the second king yet (even if we would say that this is true only for the first year, suppose the son never actually gets to the throne (we would have a document with a king that never was). How would these shtaros be dated?
(Sorry for the verbose question.)
If the only reason to mention the king in the Shtar is "Shalom Malchus", as Rashi says on 2a DH li'Melachim, then when no king reigns there probably is no Shalom Malchus, and the Shtar may be dated based on another government, or the years since the Churban, etc. According to Tosfos (ibid.) that the Shtar we are discussing has no requirement of Shalom Malchus, it is obvious that another form of dating may be used, and the Mishnah is just discussing what to do if one is dating by the king's years.