打ち合わせの日時を決めたいので、ご都合のよいお時間をいくつかくださいって英語でなんて言うの？

Asking for someone's availability is a great way to see all your options compared to their schedule to arrange a meeting. This is a polite and professional way to arrange a meeting, that also sounds very accommodating. To "look into" something means that you will spend time to find out information. It also tells them that you need to look at two schedules, yours and theirs. So if someone is demanding a time that you are not available for, this language politely informs them that you need to consider when you are available as well.

"Could you kindly tell me as soon as possible when you would be available for a meeting?" This is a great formal phrase to use every day, during business and other situations. The addition of "could you kindly" makes this a very polite and respectful sentence. "Kindly" asking someone to do something is always a wonderful way to add politeness to a sentence, especially in business. This phrase, however, does not specify directly that you are asking for a date and time for the meeting, but it is implied. Adding "as soon as possible" lets the person you are speaking to know that it is important that they get back to you quickly. Example: You: "Could you kindly tell me as soon as possible when you would be available for a meeting?" Branch Manager: "Absolutely. I will have my secretary check my schedule and contact you within the hour." "Will you kindly give me the date and time you are available for a meeting?" This is also a great formal phrase to use, and it is similar to the last one. The biggest difference here is that you are explicitly asking for a date and time, and leaving no room for misinterpretation. Again, the addition of "will you kindly" makes this a very polite sentence appropriate for business. Example: You: "Will you kindly give me the date and time you are available for a meeting?" Business Partner: "Gladly. Give me a moment to check my schedule. I have an opening on Tuesday at 4 o'clock. Will that work for you, Sir?" "Would you possibly be able to tell me a convenient time for us to meet?" This is a slightly less formal phrase you can use to ask someone about what time would be good to meet. You could still use this in business, but this would be something you would use with a business partner or other business associate you are more familiar with. "Would you possibly" implies some degree of familiarity, and doesn't express the utmost politeness. However, it is still considered polite. If you are speaking this phrase instead of using it in an email, be sure to use a cheerful tone of voice. If used in an annoyed or upset tone, this sentence can be considered rude in some cases. Example: You: "Would you possibly be able to tell me a convenient time for us to meet?" Business Associate: "Yes, of course! Hold on one moment and I'll check my schedule."

Making a suggestion in question form is a more subtle way of proposing a meeting.

This is a formal you say it. Please note you can say book/schedule or appointment/meeting. So you can use these words interchangeably.

Most business men keep a strict diary or appointment book...There are slots and times that are marked as " available"...IE free to be filled. So when we need to gather information on potential dates...We just need to ask: "what is your availability? "We really need to finalise the contract details, what is your availability for a buiness meeting?"

This question is common nowadays emailing between companies around the globe. In a formal email where the email is to a client or your superior I would say "please advise times and dates that best fit your schedule for this meeting". If you are the boss or have the upper hand, and still want to ask when suits them you can also give them a specific time, like "Does Monday morning suit your schedule/diary?"