テニスのレッスンがあり、英会話レッスンが受けられませんって英語でなんて言うの？

If you can't make or do something then it is always nice to explain why you can't do it by saying 'I have a tennis lesson' this explains why by adding 'at the same time' this means that you can't do both at the same time

"I'm afraid I can't..." is an apologetic way of putting across the information, that sounds polite. In a similar way, starting the sentence with "I'm sorry..." also conveys you are apologising, and infers that you understand it may inconvenience or affect the other person. "Unfortunately..." also conveys your apologies and sounds polite and respectful. "I can't make it to..." is a common way of saying that you will not be able to go to do something.

For most people, simply saying “I won’t be able to attend” would suffice. However, as a courtesy you can provide the reason as to why you cannot attend. Thus adding “I have a tennis lesson at that time” would be reassuring to your listener. To complete the sentence, you can simply say “I won’t be able to accept the English lesson because I have a tennis lesson at that time.”

Being polite is the key here! "I am really sorry" is a very polite way to express your regret for not being able to attend the scheduled class. "Incidentally" used in this case means as a chance or an occurrence. It can also mean "by the way" which is used to add a further remark to something already mentioned. "I apologise" is another way of saying you are sorry and it is a little more formal than saying "I am sorry" "To take part" also means to join so in this case we are unable to join the class. "To coincide" means to occur at the same time. In this case, our Engish and tennis lesson are coinciding or scheduled to happen at the same time.

Example sentences "I won't be able to take part in the English lessons because I have tennis training at the same time" and "I have tennis lessons at the same time, so I can't attend the English class" clearly explain to your reader/listener that you cannot attend the English lesson and why (because you have tennis lessons at the same time). The sentence structure swaps between the two sentences. In the first we see we cannot join and why. In the second sentence we say what our other commitment is and that we can't join because of this commitment instead. You could also add "I am sorry but" to the beginning of either sentence to add more emotion and express some sorrow for not being able to join.

In both these instances you are informing the person that you are unable to make your arrangement due to the fact that you have made another arrangement to play tennis.