You should write your availability on a cover letter at the end of the closing paragraph.
If you’re available starting from a specific date, you can write something like “If hired, I can start this position anytime after March 3rd.” And if you need to give your current employer two weeks’ notice before accepting a job offer, try writing “I can begin work with two weeks’ notice.” Are you ready to start immediately? Simply write “I’m ready to start work immediately if hired.”
However, most job ads don’t require applicants to include availability in their applications, as this topic is often discussed during interviews.