Invocations for the new pact blade... hmmm...
1) Let them turn their Rod into a Pact-Keeper, giving them a +1 to spell attacks and save DCs if they cast with their rod in hand.
2) How about letting them use their rod to grapple someone with a corruscating whip of Eldritch Power at a range of 15-20ft?
3) Rather than medium armor proficiency (And magic armor) let them get an upgraded "Eldritch Armor" form of mage armor. Instead of 13+Dex make it 10+Cha+Dex
4) Dual-Wielding invocation. If you've got a light melee weapon in your off-hand you can bonus action attack after using Eldritch Blast.