How can I break it to an employee I won't be giving them a raise without alienating them?

Ask them what they think they need to do to get a raise. Then tell them what you expect from the employe or company to do that.

Give them a path for the raise they want. If they are not the kind of employee who deserves an upward path, then alienating them is not your biggest problem.

Give them a timeline and set goals for how they can earn that raise in the near future.

The only reason I have ever done that is because of a very poor performance review and they still had the chance to improve

You must provide detail on how you came to you decision.

Explain where they missed metrics and how they can improve before their next evaluation. Centering on all positive metric and placing positive emphasis on areas of improvement.

communication. help them understand why and then help them understand how to make the necessary changes. People crave candid feedback.

The only way to accomplish this is to explain to said employee exactly why there is not a raise coming. If it's something like the company is going up for sale and they're attempting to look more profitable there for they're not or if it's that the company is in poor financial shape and cannot afford to versus just telling them you're not getting a raise.

It all depends. Did the rest of the company get a raise? If so, you better have a damn good reason and be able to back it up. If not they are part of the entire group which you can show all of them they are already over paid or expect a mass rebellion.

It depends on the reason. Is the employee’s performance not up to par? If so, then the employee needs to known this so they can make improvements. If the company fell short of their goal to pay out bonuses, then the employee needs to know it is an across the board issue. Those are basically the only two reasons I can think of that an employee would not get a bonus if it is standard for the company to payout bonuses.

Being honest with them is the best answer. Explain ways they can improve so that they can earn a raise during their next review/raise cycle.

Stress their good work, but discuss issues openly.

This is a common problem, with no easy solution. Having done this several times during my career, I believe it becomes easier if the decision is backed with facts, as to why the company has decided to not give a raise. These facts could be individual performance issues, project issues, client-related issues, ROI of the role, or overall value proposition. However, it is important to also emphasize the areas that need improvement, and if there is a marked positive development in those areas within a certain timeframe, the company would be willing to revisit the issue in due time. It is always hard to argue against facts when presented with reasoning, most employees see it as positive feedback.