The answer to this question will depend on the taxpayer status of both depositors. Unfortunately, unless both depositors are non-taxpayers, there is no way to avoid paying the taxes on the savings accounts. As always though, there are options available.
The first alternative is a fairly obvious one in that the funds should be deposited into an account under the sole ownership of the non-taxpayer. At the end of the year, the owner of the account can file the R85 form and request they not pay taxes on their account.
The other party will have to have their own account, which they will have to pay taxes on.
Another alternative is to choose a more lucrative investment option that will offset the money paid in taxes and also accumulate more earnings. Some equity-based investments will have a much higher interest rate than the standard savings account that will more than take care of the tax payment on interest earned.
If you insist on keeping the money in a standard savings account though, the only alternative in avoiding taxes on interest earned is to separate the accounts.