I need to move a clients site which was loaded into the incorrect site. I have tried to use the http://yoursite/_layouts/sitemanager.aspx site, but it states there is an error.
In your question you were not clear and did not specify which version is the sharepoint you are using and does not even need to migrate the sites between the same collection of sites.
Anyway, here is an example of how to do in sharepoint 2007, (for 2010 and 2013 the way is similar).
Go to Site Actions > Site Settings and located the Content and Structure link under the Site Administration section:
Right-click the site you want to move.
Select the option "move".
Specify the destination and confirm.
Note that the site has been moved to the desired location.