This question has recently come up again via How do i push to Amazon Elastic Beanstalk from SourceTree?, please see the answers from Seth Foss and Andrés Boedo for details, in summary:
[...] you should be able to get what you want pretty easily with custom actions.
In Windows, these can be set up in Tools > Options. For Mac, the tab is in Preferences.
In case anyone wants to do the same thing, what I created was a Custom Action, which runs the script: /usr/bin/git with parameters aws.push
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