Since this weekend (2017-11-13) FaucetHub supports the direct withdraw of BitCore coins.
Within this account you can create an BitCore withdraw address.
This address you can use for the faucets mentioned in this blogpost.
Claim BitCore at FaucetHub
All faucets withdraw directly to FaucetHub.
My favourite: Claim every 5 minutes with one easy captcha:
- WOWFaucet (withdraw required)
Solve 3 captchas: