---
"Integrated Circuit" (IC), no?
Good thought.
Since your call-waiting tone is 425Hz, one cycle takes:
1
t = ------- = 0.00235 seconds
425Hz
to complete, and since the tone will be on for 60 milliseconds, the
number of cycles during that time will be:
60ms
n = --------- = 25.53 ~ 25
2.35ms
Looking at the data sheet for the 567:
http://www.datasheetcatalog.com/datasheets_pdf/N/E/5/6/NE567.shtml
on page 5 (407) there are two graphs which show frequency VS
bandwidth and greatest number of cycles needed for output. Since
you have 25 cycles available it looks like if you set your bandwidth
for something between 10 and 14% it might work. I don't know what
effect the data signal is going to have on the 425Hz tone other that
it'll degrade its detection, so the best thing might be to just
wire one up and see what you can do with it.