How about using the 'date' command?
for example date +%Y%m%d, so something along the lines of:
zgrep "MCPKG" /centralizedlog/dsd0110{1,4}/afcdr/$(date +%Y%m%d)/*.gz |grep success > save$(date +%Y%m%d).txt
That's assuming you are looking at today's date. If you want this for day(s) in the past...