I would personally go for Createx airbrush paint on this one. Their acrylic mediums can adhere to practically anything. This one
specifically can adhere to latex, and other forms of plastic and fabric, and is meant to be flexible. It is also made of automotive grade pigments so it doesn't fade from exposure to the sun, which may be useful for a parasol (assuming you're not going for fluorescent paint, which does fade).
Your parasol is made of PVC, which has a similar exterior fabric as latex. You can e-mail those friendly createx folks to ensure the paint will work on it, I'm sure they'll simply affirm that it will.
To achieve the base umbrella colour you'll need to purchase a 5602 Opaque Base to mix with deeper pinks to achieve the pastel. It is also up to you, since you're using a transparent canvas, something I have no experience with, as to whether you'll need to paint it white before applying the pinks. It also appears that to need to seal the paint with 5604 Gloss Top Coat. This will protect the paint finish from damage and actually make it so that your umbrella is functional! As for the darker coloured hearts, I believe you could paint this createx paint manually, without an airbrush, but then the brushstrokes will be very obvious. Another option is to produce a stencil out of a semi-flexible plastic or stiff fabric and airbrush the darker pattern on.