I think what your client is asking is to select a font that would reflect the theme and characteristics of the kindergarden website.
My advice would be to use a combination of 2 fonts:
- 1 display font that reflects the characteristics to be used for headlines and titles
- 1 that would be a more default looking font(simple sans-serif or serif) to use for body and continuous paragraph text to ensure good legibility and redability
I would first find the font you want to use for titles and headlines by searching through display and handwritten font on Google fonts
Display and handwriting fonts
and then use the Popular Pairing section on the Google Fonts website to pick the best complementing font for your first font.
e.g. If you take the Gaegu font here are the pairings that Google Font offers as most commonly used
What ever Title font you pick just make sure that it is easy to read mayeby Gaegu isn't a bad choice after all.