I was searching forever for this! Finally, I just inspected the code on the calendly example sites and I was able to do it with the code below. If you're using Sqspace 7.1, the button should align with the design colors you're using in the section you place it. Customize the colors for your brand and remove <center> & </center> if you don't want to center your button:
<center><button onclick="Calendly.initPopupWidget({url:'YOURLINKbackground_color=A8D5E2&primary_color=1c6e8c'});return false;"class="sqs-block-button-element--medium sqs-block-button-element">BUTTON TEXT</button></center>