I've cut and paste some more from website I linked for you.
Your working pattern
Think carefully about the effect that part-time working would have on your employer's business. For example, if Friday is your busiest day of the week, its more likely that your employer will refuse an application to take Friday off than a quieter day. Similarly, if your job requires you to open the shop each day, your employer may well refuse an application to take each morning off. Having a clear idea of the limits to any request will help you decide what you should ask for and encourage your employer to take your request seriously. Don't damage your chances by asking for something which is clearly not going to be workable.
Costs to your employer
Your employer may have grounds to refuse your request if it would be too costly for them to reallocate your workload among other staff, for example because of overtime, retraining costs etc.
Think of ways to reduce costs to your employer. For example, could you undertake the retraining of other staff? You can also point out that your employer will make cost savings because you will no longer be getting full-time pay.
Work-life balance
You need to stress that improving your work-life balance will help your morale, motivation and commitment to the business. If you need to work flexibly because of family commitments, granting your request will make sure that you can stay with the business and are not forced to look elsewhere. It will also enhance the business's reputation as an employer of choice.
Supporting your application
Speak to anyone you know in a similar job about their working patterns and find out how they presented their case to their employer.
Use this information in support of your application. Alternatively, if their request was refused, look at the reasons given and see if these could be applied to your case. If so, think of ways around them.
Trial periods
If you or your employer aren't sure that job sharing will work, remember that you can agree to try out the new pattern for a short period. Be sure to agree (in writing) with your employer which of you has the final decision about whether the pattern becomes permanent and what will happen if you can't agree.
HTH