If a client wants to export data from AMO then you can schedule reporting templates for clients FTP to which AMO will dump desired data everyday and from there client can do an api call and get the dump and automate it as per their requirement .
Here is how you do the setup https://enterprise-intl.efrontier.com/CMDashboard/help/internal/reports/t_set_up_report_templates_fo...
Request TS to create a reporting FTP and they will allocate a location and share the credentials which can be shared to the client .