You will need a command line compression program. Personally, I use pkzip.exe because it's small and can be stored right in the mIRC folder. However, some of the larger Windows apps (such as WinRAR) have command line methods as well.
Check the documentation for whatever you want to use for what the command line is for compressing something into a folder.
Then, just use a timer:
on *:start: {
.timerZipLogs 0:01 0 86400 ZipLogs
}
alias ZipLogs {
if ($date(dd == 01)) {
compress commands here
probably also use a /remove command to delete the logs afterwards if you want to
}
}