How can I get a persistance cookie when a pool member is selected by an iRule?

Here's a framework that may work for you.

when HTTP_REQUEST {
    if { [string tolower [HTTP::uri]] starts_with "/public2" } {

         set the desired pool
        set this_pool "local-pool"

         send traffic to pool and specific member
        pool $this_pool member 10.70.0.3 80

         if persistence cookie doesn't exist, set a flag to create one
        if { not ( [HTTP::cookie exists BIGipServer$this_pool] ) } {
            set insertcookie [list $this_pool "10.70.0.3" "80"]
        }
    } 
}
when HTTP_RESPONSE {
    if { [info exists insertcookie] } {
         encode the IP
        scan [lindex $insertcookie 1] %d.%d.%d.%d a b c d
        set ip1 [format %02x $a]
        set ip2 [format %02x $b]
        set ip3 [format %02x $c]
        set ip4 [format %02x $d]
        scan $ip4$ip3$ip2$ip1 %x ip

         encode the port
        scan [format %04x [lindex $insertcookie 2]] %2s%2s e f
        scan $f$e %x port

         insert the cookie
        HTTP::cookie insert name BIGipServer[string map {"/Common/" ""} [lindex $insertcookie 0]] value "$ip.$port.0000"
        HTTP::cookie path BIGipServer[string map {"/Common/" ""} [lindex $insertcookie 0]] "/"

         unset the variable
        unset insertcookie
    }
}

Based on some logic in the HTTP_REQUEST event, I set a flat (insertcookie) that is picked up in the HTTP_RESPONSE event. Using the following documentation:

sol6917: Overview of BIG-IP persistence cookie encoding

the HTTP_RESPONSE event encodes a persistence cookie the same way the cookie persistence profile would do it so that it's natively picked up and used. You'll need to apply the basic cookie (insert) persistence profile to the VIP. Perhaps the most interesting thing about this method is that you don't have to make any provisions on the request side to persist to a given pool member. The cookie name and value allows it to happen automatically. That said, this method isn't really required. You could have just as easily created your own cookie (with any value) in the response event and handled its return in the request event.