can you please let me know from where we can download the Appian common objects?

Go to Records -> Appian Software -> 7.9.
It's available under Add-ons section

Thank you. It looks like there are no Add-ons for 7.10. If we are using Appian 7.9 can we still use the Add_ons under 7.9?

Yes, it should still work. If you open the documentation, Appian 7.5 is listed as prerequisite. This application may not have been updated since 7.5. I think this is not supported by Appian technical support either.