I've found it really hard to think of songs I like that I think would suit Neil's voice! But here are a couple - Champagne Supernova by Oasis, Flame Trees by Cold Chisel, & Bizarre Love Triangle by New Order.
[Of course most of their cover choices are reliably good, eg. Throw Your Arms, Everybody's Talking and Neil's take on The Smith's There Is A Light That Never Goes Out (on Seven Worlds)]
P.S. Anyone looking for a great, if somewhat left-of-field cover, I recommend they check out Ben Folds and Rufus Wainwright's cover of 'Careless Whisper' on youtube!