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If you're willing to muck with the transaction processing code, you could only allow transactions to addresses that have been created and blessed by the Central Authority. You'd have to also teach the wallet code not to create lots of addresses, but if you're going to require users to register and not be anonymous you might as well centrally create and issue them their wallets.
You then need a mechanism to broadcast new, blessed public keys to the entire network, but that might be as simple as generating a transaction from a baked-in blessed address (owed by the Central Authority) to the newly created blessed address.
Implementing and debugging would be a lot of work, and I'd be nervous about neglecting some little detail and leaving the system open to hacks (Bitcoin is nice because so many people are extremely motivated to find any chink in the system and either exploit it or patch it-- a small complementary currency wouldn't have that advantage). But it could be done.