The consular year began for the "ordinary" consuls on 1 January; suffect consuls then replaced them at various dates in the course of the year.
Strack,
Trajan, p. 18, note 40, following
Mommsen, Staatsrecht I, 588 f., says that consular elections, including those of the emperors, took place at assemblies in either March or October of the year preceding the consulship. He cites e.g.
military diplomas that do not yet name the emperor
consul designate on 14 August and 10 October in the year before their consular year.
I think it unwise to assume any regularity in the dates when emperors were elected to consulships, however. Emperors could be designated to the consulship as early or as late as they liked.
The
second Triumvirate, for example, divided up the consulships years in advance, whence Antony frequently has the title
COS DESIG ITER ET
TER on
his coins.
Caius and
Lucius Caesars, when they assumed the
toga virilis at around age 15, were designated consuls for the years they would become 21, and so on.
Nero hastily assumed a fifth consulship to counter the revolt of
Vindex and
Galba in
spring 68.
There is little evidence for any regularity in the dates when emperors were designated to consulships, but
plenty of evidence for exceptions and caprice.
Designations on coins more or less end with Commodus'
COS V DES VI of 189.
Gallienus has a very
rare VII DES COS, Goebl 1231A.