Your best bet would be to auto-import the Blogger RSS feed. You’ll set up a cron job in WordPress to check the Blogger site’s feed for updates and, if they exist, create a new post with that content.
There are a handful of plugins already out there that will do this for you, but essentially, here’s what you do:
- Every 1 hour/2 hours/6 hours/whatever, load the RSS feed from the remote site.
- Check to see if there are any new entries
- If there are, use
wp_insert_post()to create a new post with the imported content
There’s a premium plugin called AutoBlogged that does this for you.
You can also use Feed WordPress to update your site from an RSS feed on whatever interval you want.