Not really a bitcoin faucet, but consider to you high paying altcoin faucets. You can transform the coin into Bitcoin then.
NEM Faucet: 100 XEM a day, 1 XEM is currently around 105 Satoshis, so you get more than 10k a day with one request.
NXT Faucet: 4 NXT a day. 1 NXT is currently around 1,5 Satoshis, so you get around 6k Satoshis with one request.