How to implement a counter Button in roMessageDialog

You'd need to use multiple-layer menus, or design a custom roscreen or roimagecanvas to utilize more buttons.

which would be the best way to make this possible

Easiest is multiple dialog screens - have button 8 be 'more choices'

this code

Function ShowMessageDialog_ChooseQuality(episode) As Void
    port = CreateObject("roMessagePort")
    dialog = CreateObject("roMessageDialog")
    dialog.SetMessagePort(port)
    dialog.SetTitle("Choose Links")
    dialog.SetText("Choose the video Links to play")
 
    count = 1
    for each stream in episode.streams
      dialog.AddButton(count, ValidStr(stream.texturl))
      count = count + 1
    next
    dialog.EnableBackButton(true)
    dialog.Show()
    While True
        dlgMsg = wait(0, dialog.GetMessagePort())
        If type(dlgMsg) = "roMessageDialogEvent"
            if dlgMsg.isButtonPressed()
                index = dlgMsg.GetIndex()
                if index >= 1 and index < count
                    dialog.close()
                    retval = ShowVideoScreen(episode,episode.streams[index-1].url)
                    exit while
                end if
            else if dlgMsg.isScreenClosed()
                exit while
            end if
        end if
    end while
End Function

I'd just check for more than 9 bitrates being available, and if there were more than 9, I'd split them in some logical order like displaying the top 8 and the lowest available, or every second bitrate, or every third, or something consistent.
Or -- as suggested, take the first 8, make 9 be more choices, pass the remaining bitrates to it, and loop the thing back to the first page until you're out of options.