The best replacement for stateless is stateful firewall.

The best alternatives to stateless are rated as following:
★★★★★  stateful firewall
★★★★★  stateful packet filtering
★★★★  stateful ipv6
★★★★  stateful
★★★★  stateful protocol
★★  stateful ejb
★★  stateful session bean
★★  stateful web application
★★  stateful server
★  stateful web service
★  stateful java
★  stateful dhcpv6
  stateful servers
  requestscoped
  stateful application
  stateful firewalls
  statefull
  stateful connections

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Google Trends

Scale is based on the average worldwide traffic of stateless in all years. Click on graph for more.
stateless
stateful firewall
stateful packet filtering