There's nothing you can do to prove that she will not overstay.
The application needs to show that there are sufficiently strong ties and compelling reasons to return home. Sufficient to convince the ECO.
Strong ties and compelling reasons differ from country to country, city to city, individual to individual. Some examples of ties can be a job, a house, a family, a bank account.
"Ties" are the various aspects of your life that bind you to your country of residence: your possessions, employment, social and family relationships.
You may have assets, unmarried children, relatives, who are in your home country for whom you may need to return.
The UKBA page specifically for the General Visitor is here
It's well worth taking a look and checking out all of the links provided.
Here is the UKBA Guide to Supporting Documents for visiting the UK
UK family members can sponsor the applicant by providing an invitation letter to confirm the relationship, purpose of the visit, reasons for the timing and also the support they will be providing in terms of financial assistance and/or accommodation.
I would suggest that a sponsor needs to provide details of accommodation (owned or rented), 6 months bank statements, 6 months pay slips, employment details,proof of address documents etc. Plus a good supporting letter.