That’s not exactly a WordPress problems, and it would be easier to upgrade MySQL on the server, to be honest.
You need MySQL 5.5.3 or higher to support the utf8mb4_unicode_ci collation.
Have you contacted your hosting provider?
Alternatively, you can try changing your collation to utf8_general_ci but that might cause character encoding problems with the existing data.
Unfortunately the hosting provider will not upgrade MySQL and basically said “Google it”.
Ok, so on the old database I recommend changing the collation on the tables to utf8_general_ci and then export again.
Alternatively, move just the content by exporting/importing in a fresh installation via the Tools section of each blog’s Dashboard.
Or, alternatively, find a nicer hosting provider. 😉
James, thanks for the responses. I was able to get it working and posted how in this thread in case it works for others too.
Unfortunately I don’t always have control over the client’s hosting provider but when I do I will start considering MySQL 5.5.3 or above a prerequisite to be considered an appropriate WordPress hosting provider.
Thanks for sharing your solution!