Ideally what you want is Remote Traffic Mirroring which the 2600's don't support.
What you could try though is putting your mirror-port in a different VLAN and connect those mirror ports up to a 4th switch which then mirrors to another port and connect the appliance to that. Alternatively you could use a hub instead to simplify it. If the appliance is simply doing passive monitoring then that should be okay.
You could also try something like this:
Switch 1 - mirror port 48, port 48 untagged VLAN2, monitor VLAN1 - connect port 48 to port 48 of Switch 2.
Switch 2 - mirror port 49, port 48 and 49 untagged VLAN2, monitor port 48 and VLAN1 - connect 49 to port 48 of Switch 3.
Switch 3 - mirror port 49, port 48 and 49 untagged VLAN2, monitor port 48 and VLAN1 - connect 49 to appliance.
I've never tried this so I'm making no promises that this will work.
With this type of topology you can't enable spanning-tree as it will block ports that you don't wish to be blocked.