Thanks for your query.
If you have had the copper coil in for years ( which is most probably the case ), then yes, you need to give your body a rest, and let the hormones stabilize.
What you can do is take a couple of months off.
Meanwhile use barrier methods
Insert the Mirena
or take the Depo shot once your period begins after a couple of months.
Do beware of the inherent side effects of Mirena / Depo too.
The commonest is irregular menstrual bleeding, including absence of a proper period for prolonged intervals.
All the best.