i dunno about installation..
but i wound not suggest coilovers on KYB or Tokico... those shocks are too soft for coilover.. your car will bounce like hell..

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personally i don't like coilover

: .. unless it comes with shocks that will work perfectly with the coilover ...
Eibach + KYB GR-2 or H&R/B&G + Tokico are good for 01 corolla..
and they will be best match (i mean the struts and springs)
good springs/coilovers or good struts only won't work good.. maybe worse..
the most important thing for doing suspension mod. is proper match of the springs and strut