Also it is said that Shaneeswara Swamy is a very great devotee of Lord Shiva. As mentioned in the "Navagraha Pidahara Sthothram" of "Brahmanda Purana", anybody who chants the following sthothra is relieved from all the ill-effects of Shaneeshwara Swamy placed in bad houses.
Suryaputhro Deerghadeho Vishaalaakshah Shivapriyah | Mandachaarah Prasannathmaa peedam harathu me Shanih ||
सूर्य पुत्रो दीर्घ देहो विशालाक्षः शिवप्रियः। मन्दचारः प्रसन्नात्मा पीडां हरतु मे शनिः ॥
One who prays to Lord Vishnu is protected from Shani as he is said to be a great devotee of Vishnu. (It is interesting to note that Hanuman Himself was devoted to Lord Rama, an avatar of Vishnu).
It is also a wide spread belief that one who is an ardent devotee of Lord SriLakshmiNarasimha Swamy or Lord Venkateswara (Balaji) is also always protected by Sri Shani Maharaj.
Except for prayers to Lord Hanuman, Lord Shiva and Lord Vishnu you can also chant mantras for Shani to relieve the ill effects of Shani.
Mantra for Shani : Aum praang preeng proung sah Shanaye namah Neelaanjan samaabhaasam raviputram yamaagrajam, Chaayaa-maartandam-sambhootam, Tam namaami Shanaishcharam.
You can chant this mantra for at least 7 times a day, because Shani is the 7th planet counted starting from the Sun. However, if you are troubled by Shani it would be better to chant the above mantra for 108 times a day.