Thank you for reaching out to Constant Contact API Developer Support, my name is Caleb. My team is here to assist outside software developers with questions about building into Constant Contact's API.
We do currently have a plugin that would allow you to syncronize your contacts from Magento to your Constant Contact account, however this plugin requires that you use a newer version of Magento which is version 2.4.1 or above.
Connecting Your Magento Store: https://knowledgebase.constantcontact.com/articles/KnowledgeBase/41006-Connect-Your-Constant-Contact-Account-with-Magento
If you are unable to update your Magento store to a newer version an alternative method would be to develop a plugin yourself using both Magento's APIs as well as our own.
Magento API Starting Guide: https://devdocs.magento.com/guides/v2.4/get-started/bk-get-started-api.html
Constant Contact API Quick Start Guide: https://developer.constantcontact.com/api_guide/getting_started.html
The final option would be to search for an existing third-party plugin that would connect your store to your Constant Contact account that meets your current store's version.
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