1. I am writing up today's diary.

2. I am keeping today's diary.
3. I am writing down today's diary.
4. I am writing today's diary.

Which expressions are correct?

To make #s 1, 3, and 4 correct, you'd have to add the word "entry" after the word "diary."

The expression is that you "keep a diary" -- or you "write a diary entry" or "write an entry in your diary."

=)

this is the year i was born 2007

and still noone answer him

yes

ik this answer is old but im pretty sure this was an interaction of multiple people before jiskha developed this format

All four expressions can be considered correct depending on the context and what you want to convey:

1. "I am writing up today's diary" implies that you are currently working on writing the contents of today's diary entry.
2. "I am keeping today's diary" suggests that you are actively maintaining a record of your daily experiences in your diary.
3. "I am writing down today's diary" means that you are in the process of writing down or recording the contents of today's diary entry.
4. "I am writing today's diary" simply states that you are writing a diary entry for today.

It's worth noting that while all four expressions convey a similar idea, the nuances and emphasis may differ slightly.