It's hard to suggest a middle name when you don't know the last name as well (you like to take into account the "word" that the child's initials will make, and, more important, the sound and rhythm of the whole name when it is spoken aloud). Without benefit of last name, however, how about selecting a second gaelic name -- either a name that is usually a surname like McCullough, McKennan, or Lachlan; or a name that is usually a given name like Eamon or Kael or Kieran? They all sound good with Konnor -- at least as far as we can imagine the sound without the last name!
aside: meanings can be interesting
Connor (and I presume Konnor) = much wanted
Mc = son of; Kennan = handsome
Mc = son of; Cullough or Cullach = boar (figuratively, McCullough has meant a brave man)
Lachlan = from the lake
Eamon = wealthy protector
Kael = mighty warrior
Kieran = little dark one (as in black hair)