What antidepressants will not affect libido.?

There May be One. Viibryd/vilazodone in all the clinical trials & my experience over the past 8 months or so (since it came out) does not appear to cause sexual dysfunction. Also, wellbutrin/bupropion is very unlikely to do so as well.
It depends. A number of antidepressants may affect libido - some of the newer generation ones seem to have less effect. Many people have used medicines such as wellbutrin (bupropion) with good success. You really need to discuss what type of ill effects you are having with your current medicine so that you and your physician can make informed decisions.
All have risk. All antidepressants have a risk of affecting libido or sex drive. Some are just less likely than others of having such an effect. The antidepressants with the lower libido side effect risk are wellbutrin/bupropion, celexa/citalopram, lexapro/escitalopram, and effexor/venlafaxine. I sometimes prescribe wellbutrin to both augment a current depression treatment and counter sexual side effects.