The amavasya of hindu month "Jyestha" is the birth-date of Shani grah. Worshiping Shanescharan on his birthday is definelty a good remedy .
Rituals for shani jayanti:
1) doing abhishek of shani grah with oil.
2) Reciting shani graha stotra/chalisa/kavach etc.
3) fasting on this day
4) worshiping Hanuman, rudra , kali and bhairav jee is also auspicious for shani grah related problems. in this worshiping hanuman ji with bajrang ban and chalisa and rudrabhishek for shiv ji is the best n safest remedy.
5) And helping labour class people is one thing, which will definetly please shani
6) feeding ants , crows n black dogs.
Om neelanjanam samabhasam ravi putram yam aagrajam,
Chaya maartan sambhutam tam namami shaneshcharam.