1. I'm booking a couple of tickets tomorrow coz it'll sell out.

2. I'm booking a couple of tickets tomorrow 'coz it'll sell out.
3. I'm booking a couple of tickets tomorrow cause it'll sell out.
4. I'm booking a couple of tickets tomorrow 'cause it'll sell out.
[Which ones are grammatical? Do we have to use an apostrophe?]

All of them are slang and not used in standard writing. You need to use "because."