Here are three options for you using SPSS:

Do not use the method shown in the following video--it is not correct. 

• https://www.youtube.com/watch?v=-dSoWqDyT4E

The method shown in that video yields a CI that is symmetrical regardless of the value of r. The correct method yields a symmetrical CI only when r = 0. Otherwise, the side of the interval toward 0 is wider--see the attached image.

HTH.

I no longer use SPSS (partly because it is a pain to do this sort of thing). It would be simpler to do this in R (or even in Excel). You can do this using compute commands (see link) and there may well be macros.

I attach a simple excel calculator I wrote for this a while back (though in practice I would use R).

Here are three options for you using SPSS:

Do not use the method shown in the following video--it is not correct. 

• https://www.youtube.com/watch?v=-dSoWqDyT4E

The method shown in that video yields a CI that is symmetrical regardless of the value of r. The correct method yields a symmetrical CI only when r = 0. Otherwise, the side of the interval toward 0 is wider--see the attached image.

HTH.

The online calculator at http://vassarstats.net/rho.html does the job for me. The site does state that  "the confidence interval of rho is symmetrical around the observed r only with large values of n".  I did not face this problem with a sample size up to approx. 100. For greater sample sizes, the links provided by Bruce might be more appropriate.

All the best.