If you're asking the question not long before July, then you didn't plan properly, and so now, we're back to basics. This is the kind of thing you know in advance is going to come up. There are certain times of the year when everybody wants to use vacation days, and you already know what the biggies are. Christmas, Thanksgiving, New Years, Memorial Day, Fourth of July. Nobody should be shocked or surprised by this.
There are a number of ways to handle it so that it's not an issue, but however you choose to go about it, you need to be upfront with your workforce and have good, clear communication. Here are two possible solutions for you to consider. Depending on the particulars of your company, you may find that one works better for you than the other. Personally, I'd recommend using them both in tandem.
Bonuses Offered & Fixed Slots
Let everybody know during new hire orientation, and periodically thereafter, that there are certain times of the year when, for business reasons, there will only be a limited number of “vacation slots” available, and these will be doled out on a first come, first served basis. To provide some incentive that will help prevent logjams, offer an economic incentive to show up for work on the days in question. Time and a half, free lunch and dinner, gift cards, or all of the above.
This works because everybody knows in advance how many “slots” there are during the key times, and know that if they don't act quickly, the spot they want might already be taken.
Stand Clear
Depending on whether or now you've empowered your employees, and to what extent, you can simply provide a whiteboard calendar for each functional area and let them work it out amongst themselves, with management oversight in the event of conflicts or problems.
This, of course, only works if you've actually empowered your employees, but it can be the very best way to ensure equitable outcomes. By letting your employees work these sorts of things out on your own, not only do you let them have some control over their own destinies, you get a fantastic opportunity to identify leadership traits in your own people that may not have been readily apparent before.
What I personally found that some people self identify as mediators. When conflicts arise, before management can even get involved, your mediator employees will step in and smooth things over. It's a fascinating process to watch, and this idea alone can reshape your entire organization. Even better, it can point you to the exact individuals you should be grooming for advancement.
There's nothing better than a win-win scenario. The employees win because they get to work it out for themselves and show you what they're made of without being treated like kids on the playground. It's growth and development under the RADAR. You win because empowered employees are more efficient, effective, and productive.
