My ultimate plan for my hair is to have it chocolate brown with a chunk of a soft pink on the side. I really liked how carnation pink looked on the website, however I was disapointed to find out that its currently sold out.
From your experiences, what are some alternative techniques for achieving a soft baby pink?

You could get a darker pink and some white toner and mix to your liking. Make the mixture slightly darker than you want your hair to look.

You can do this with conditioner but the results are so much more unpredictable since the thickness of the conditioner varies so much. For this reason I recommend using a white toner from the same range which will have the same consistency as the pink colour.

I have tried this myself with variable results. The result will probally fade quickly since very little pink is present to have a sofy babay pink. Also probvally will be much darker than would like at present but semi-permanents do fade. One suggestions is to start with a light pink shade like Bubble Gum Pink, Cotton Candy Pink, or Cupcake Pink and leave on for 10 to 15 minutes only maybe less after a strand test is performed. Strand test is apply the dye to a small section of hair and leave on until get the shade you want and mark the time needed. Then mix the remaining idye ingresdients and apply over all the hair.

A second method if live in US and near a Sally's Beauty Supply or other open to public beauty supply store is to get a red colored shampoo that deposits red onto the hair. Wash only the bleached blonde strand with the red shampoo. Suggest the blonde should intially be as light as very light beige blonde to platinum blonde otherwise you will have strawberry blonde. Saturate the hair almost to the point of dripping but not quite, comb through and leave on for 15 minutes or 30 minutes after a strand test is a suggestion. I am not a professional only offer suggestions. Good luck.

I adore atomic pink, but it's dark, but you could mix with white toner as jude said?
SFX cupcake is an awesome dye too :D
And, I loved the color when I bleached my atomic pink!
I had to re-dye it though, cause my roots went white but they were virgin, the atomic just came out amazing.