Cyanotypes may not be archival, but I have one that's still very blue after more than 120 years! From the buildings in the picture the negative must have been exposed before 1870, so I assume the print was made not too many years later.
Different papers behave differently in different toners. Ilford MG IV RC hardly reacts to anything, and Bergger Art Contact reacts extremely quickly and goes violently blue within seconds - in old weak toner that doesn't affect other papers at all.
Somewhere between those two extremes you should be able to find a paper that gives nice, controllable tones.