Store a counter somewhere, depending on if you want it in sequence at the application scope level across user sessions or at the session scope layer where each user session starts at 1, 2, 3...
Then use modulo arithmetic on the counter and total number of records to pick the record to display.
SESSION Example:
<cfparam name="session.myCounter" default="0" />
<cfquery name="myQuery" ...>
select someColumnName... from someTable
...
order by someColumnName
</cfquery>
<cfif myQuery.recordCount>
<cfset variables.myRecordID = session.myCounter % myQuery.recordCount />
<cfset session.myCounter = session.myCounter + 1 />
<cfoutput query="myQuery" maxrows="1" startrow="#variables.myRecordID+1#">
<!--- +1 because modulo is zero based, CF queries are one based --->
#someColumnName#...
</cfoutput>
</cfif>