Dear Biz to Psych:
We are intrigued by your plans. We are not sure if you want to do a Bahelor's or Master's in Child Psychology. Your eligibility would depend on your specialization in your Bachelor's degree.
Psychology as a whole, or certain specializations in Psychology, and depending on the country, is classified as a program in Humanities or Sciences. You can find the list of such colleges in the US and UK in the
iMahal Education Section. Here, you would also find an overview of the education systems.
We are not aware of any reputable distance learning degree programs.