First and foremost, Cassius is, as Caesar himself has recognized, a young man who "has a lean and hungry look" (I,ii,194). Thus, he is ambitious, envious, and self-serving. Therefore, let your diary entry reflect these aspects of his personality, as well as his arrogance which he demonstrates in his conversation with Casca, who in Act II, Scene 3 asks Cicero,
Are not you moved, when all the sway of earth
Shakes like a thing unfirm?(I,iii,3-4)
Then, when Cassius speaks to Casca, he boasts that he has
...bared my bosom to the thunder-stone;
And when the cross blue lightning seemed to open
The breast of heaven, I did present myself
Even in the aim and very flash of it. (I,iii,49-53)
With the most salient characteristics of Cassius being his envy or Caesar's power, his own desire to claim such power, and his scorn for fate, your diary entry should reflect this. And, since it is a personal diary entry, Cassius will write his true feelings; thus, it does not seem necessary that he present noble reasons for killing Caesar. Instead, he may pride himself on how he has manipulated Brutus in Act I, Scene 2, in what is known as "the seduction scene." Also, he will pride himself in how he has defied the fates and rid the Romans of the "Colossus" of "immortal Caesar" which, as he has told Brutus,
Men at some time are masters of their fates;
The fault, dear Brutus, is not in our stars (I,ii,139-140)
In fact, this line may be a good beginning to the diary entry. For instance,
With this assassination, I have proven what I told Brutus; we are masters of our fates!
Cassius in Shakespeare's Julius Caesar actually conspires against Caesar, mostly, for personal gains--political power and money. In terms of how he acts toward Caesar, he does not act as a noble Roman should, although he will act nobly later as his death approaches. He might write a diary about how excited he is about the possibility of attaining more political power and more money. If you choose to go this direction with your assignment, you could just pretend you're Cassius and write about those possibilities, since he doesn't really talk about them in the play--they are suggested, not directly stated.
But when writing a diary, he might also rationalize and create more noble reasons for assassinating Ceasar. If you choose this direction, you need to see the reasons he uses to justify killing Caesar within the play. The most important scene to look at is Act 1.2, during which he introduces the idea of the assassination to Brutus, and begins the process of convincing Brutus that Caesar needs to go.
The conversation begins at line 25. Cassius first tries to get a feel for how Brutus currently feels about Caesar, by asking him if he wants to go watch the crowd honor Caesar. But the process of convincing Brutus starts at line 51. He praises and flatters Brutus, talks about Caesar being just another man, no better than he is, and outlines the danger of one man having too much power. You can simply read this passage and write the diary based on Cassius's words.
Whichever direction you choose to take, you should have plenty of details to use in your diary--and at least you don't have to write it in Latin.