Hi Dakota,
If my understanding is correct, then you mean you want to send a Card via message or, as a message response to a space or, to a direct contact.
If yes, it's very much possible and we've the /create-a-message REST api endpoint as provided here - https://developer.webex.com/docs/api/v1/messages/create-a-message
This API helps to create a message to any space or, to a person directly using his/her personId or, personEmail.
If you check the very last field/attribute for this API, it's "attachments".
So, in the attachments field, you can keep the code block for your Card and Run the API with POST request and instead of message, a card should be sent to the Receiver.
Hope this provided information help you here.
Any further assistance on this, please let us know by replying back on this question.
Regards,
Sandip