Captcha is one plausible solution, but most humans don't like it.
How about instead if you add some intelligence to your system?
Implement a cooldown between emails. Before sending an email, wait one minute. If another email request comes then wait another minute and don't send the first one. (This could be another form of attack but only if this is the only line of defense).
Would a person try to register 30 times in the last minute? No.
Would a person re-register if the last register was successful? No.
You can also combine these with the IP of the registering user: Would a user try to create 10 new account for other users from the same IP in 10 minutes? Unlikely.
If this is a corporate website and you MUST prevent the email spamming, then consider secondary ways of communication. For example, if you have the means, you can request the user to SMS the email address to a specific number, which would create a reset password request.
You could also, upon the user completing the registration, generate a list of numbers that should be used to retrieve the account. Something like: "If your account is lost, it can be retrieved by entering one of these numbers into the RETRIEVE field" And then provide a list of numbers that would be confidential to your company and the customer. The same way Google does it.
Although these mechanisms can become complex, they will be smarter than any captcha; will be easier to adapt, and more comprehensive. On the plus side your users will thank you for not having to read twisted images of numbers and letters.