Use a local dev version that matches your actual live version.
Alternatively, bug your web host to upgrade your live site to a newer version of MySQL. You want 5.5.3 or later. Preferably much later.
This doesn't fix the problem. Like @jtleathers said, sometimes the client has a MySQL version that we can't control.
So basically the latest Wordpress is not compatible with MySQL < 5.5.3 at all? That seems like a pretty major change.
Is there an easy way to downgrade your Wordpress version?