Here's a great resource for you:
In general a healthy, anti-inflammatory diet and lifestyle help boost the immune system and naturally increase platelet count.
Leafy greens, berries, veggies, omega-3 rich foods (chia, hemp, walnuts, oily fish), vitamin C, reishi mushroom superfood, are a few good foods along with exercise, sleep, and stress reduction.
Other superfoods I've seen in my reading include:
Spirulina or Chlorella. Bee pollen, which is also a source of amino acids, vitamins and other substances have been shown beneficial for the process of hematopoiesis.
Ashwagandha, a plant that is used in Ayurvedic practice, is a powerful adaptogen and is known to increase platelet count.
As always, consult your Dr. before making any dietary changes.