Unfortunately, you cannot increase the "chance of" knockdown in Axe. KB IOs will increase the magnitude and start causing knockback instead.
You best bet is to slot heavily for recharge, whether global or per power or both, and rely on spamming attacks. Attacking more gives more chances for KD.
I would also slot a damage proc or two into your fast recharging attacks in Axe to give you a higher change for greater damage due to lethal damage being heavily resisted.
Slotting knockback into your attacks won't keep them down longer, but will knock them all over the place (away from you). This in itself could be considered "longer" and combined with Chilling Embraces aura effects would certainly be a great mitigator.
However AOE based classes will absolutely loathe you 
As for Axe I suggest slotting Kinetic Combat into your melee attacks (4) which will give you health and pretty decent smash/lethal defense to layer on top of Ice's typed defenses.
Since the Ice primary is really good on endurance due to Energy Absorbtions (and if you can afford it) I suggest slotting Obliterations (6/6) into your PBAOE attacks (I think Axe gets 2 or 3 PBAOE rated attacks). While the big defense bonus at the end is positional you still get half that in typed defense and that's usually Ice's problem (getting typed defenses to the soft cap of 45%).
Pacing of the Turtle has a -recharge proc IO which is fairly cheap and Impeded Swiftness has a chance for damage proc, both of which fit quite nicely into Chilling Embrace.
If you get Icicles a neat trick there is to put 3 slots aside for the Eradication, Obliteration and Scirroco's Dervish proc IOs (energy, smashing, lethal respecitively).
I generally find the Ice primary fun to slot because there are a lot of ways to be inventive and not much concern for endurance issues.
I am currently leveling an Ice/Axe tanker and was wondering if I could get some help with slotting my axe secondary. I realize that axe is all lethal damage and one of the higher resisted damage types in the game. However, I was wondering if it would be possible to get a heavier slotting of knockdown through IO's and IO set bonuses in order to keep mobs on there butts for a majority of the fight. If anyone has good advice or information on this subject that would be awsome. Any other advice on axe secondary or ice primary is much appreciated thank you.