Morris grew up in Lanigan, Saskatchewan. In 1998, Morris played in Ontario, and played in the provincial Scott Tournament of Hearts, as an alternate player for the Cheryl McBain team. She would later move to Alberta. Morris joined Bernard in 2005 after playing for Heather Rankin. She has since been to the 2007 and 2009 Scotties Tournament of Hearts as a member of that team. At the 2009 Tournament of Hearts, Morris was presented with the Marj Mitchell Sportsmanship Award.
On February 8, 2011, it was announced that the Bernard team would disband at the end of the 2010–11 curling season. Cori has joined a new team for the 2011–12 curling season,playing as lead under Dana Ferguson.