Has the longevity of the british monarchy been the results of limits placed on it by the constitution?in terms of Charles I & II and James I & II

To begin with, England does not have a
constitution.

At one time the monarchy had unlimited
power.  Over time, their power was limited by various enactments of Parliament.  The
Magna Carta was the first document that began this
process.

In reference to your specific Stuart kings,
Charles I learned the hard way what it was like to go too far.  His forces were defeated
by Oliver Cromwell and the Round heads.  He was put on trial and found guilty and
beheaded.  This break in the power of the monarchy was known as the Commonwealth. 
Eventually, the English people welcomed the Stuarts back to the throne aka the
Restoration.  Charles II became king but his power was
reduced.

Whereas our government has a constitution, England
has a series of documents which are their guidelines.