One possible version：

Dear Tom,

Thanks for your invitation. I’m sorry I can't have a picnic with you at the weekend.I'll be busy  that day. I have to have a piano lesson on Sunday morning. After that, I’m going to play basketball with my friends. My sister is going to be 12years, and we will have a party for her. So I will go to the party on Sunday afternoon. Because I need a lot of things, I’m going to go shopping,and buy them. At night, I’m going to revise(复习) for the English test. It is very important for me.

Can you have a picnic with me next Saturday ?

Yours

Peter.

题目分析：这是一篇给材料作文，汤姆写信给彼得说明不能和他一起去野炊的理由。结合所给材料，可知本文主要考查一般现在时态，人称为第一人称，注意主谓一致问题，句子结构主要为系表结构和动宾结构，注意一些常见句式的应用，比如： I have to......； I’m going to......； we will.....及Can you......？等句式的应用。写作中注意运用代词，注意多种句式交替运用。写作中注意叙述顺序，符合逻辑关系。

【亮点说明】本文结构紧凑，语言简练。开头感谢彼得的邀请，接下来说明周末不能和他一起去野炊的理由，最后邀请他下周末一起去野炊。此处用了have a piano lesson，on Sunday morning，  a lot of 及go shopping等这些词组的运用也让文章增色不少。