Throw "constant" out. The word "constant" is time related.
It does not apply to the "rule" you have in mind. If you
change the voltage or the resistance the current will also
change. Do NOT state "current is constant in series".
Current in a series circuit is _the same_ everywhere in the
circuit. That is location related, not time related. Current
will be the same at every point in the circuit at any given
instant of time, whether the voltage or resistance varies over
time or not. It is *far* better to say "current is _the same_
everywhere in a series circuit" than "current is _common_ in
a series circuit".