If you want to be a Carpenter and have found a job to apply for then you will already enjoy working with wood and making and installing wooden fixtures and fittings as part of different projects.
It is not necessary to have a formal qualification, usually clients or employers what to see what onsite experience you have had previously or you may be able to become a Carpenter through an Apprenticeship scheme.
Please see below an example cover letter which you could use to support your application:
Cover Letter: Carpenter
Re: Application for a Carpenter
I have seen your advert in (where) and I would like to apply for this role.
I have always had a keen interest in working with wood from a very early age at school. I have now gained some more work experience working with other carpenters/joiners and this is something I now want to pursue.
I have a creative nature and enjoy making wood work look right for a client as per their specifications and wishes.
I pay great attention to detail and have good mathematical mind and am able to work out measurements and figures as necessary.
(Specify what skills you have and what you have done as part of a Carpentry role in detail, cross check with the job description and ensure that you can answer the skills and requirements that they are seeking)
I am a very confident and hardworking individual and am looking for a stable career and prepared to work very hard in this area to continue learning and improving my skills for a company.
If you are interested in my skills please do not hesitate to contact me.
I look forward to hearing from you.
Good luck with writing your covering letter.