Saturn enters the star constellation of Rohini once in every 30 years.
This is one of the most dreaded transits of the kings and his kingdom. The scriptures say “Kings will die and kingdoms will fall when Shani enters Rohini.” Last time it entered Rohini on 22nd May 2001.
On the night of 1st June 2001, the entire Royal family of Nepal was wiped out. It was followed by the death of the Indian Congress minister and Raja of Gwalior Sri Madhav Rao Scindia on 30th September 2001 in a plane crash. Then came the 9-11-2001 strike by Osama Bin Laden.
It is said that during the reign of King Dasaratha when Shani was about to enter Rohini Nakshatra, King Dasaratha worshiped Shani and pleased with his prayers Saturn did not enter Rohini during the reign of King Dasharatha. Hence the Dasaratha Shani stotras are considered an excellent remedy for Saturn related troubles.
The following is from Skanda Purana.
Shani Shodasanama stotra
Kona shanaischaro mandah chhayaa hridayanandanah
Maargandaja sudhaasouri neelavastraan janadyutih
Abrahmanah kroorakroora karmaatangi grahanaayakah
Krishnodharmaanujah shantah shushkodara varapradah
Apart from this reciting the following dashanama stotra of Shani by Dasharatha near a Peepal tree is also a highly recommended one.
Shani Dasanaama Stotra
Konastha pingalobabhruh
Krishnoroudraantakoyamah
Souri, shanaischaro mandah
Pippaladishu sansthitah
Dasaratha Shani Stotram
Om. Asya shree shanaishchara stotrasya
dashratha rishi
shanaish-charo-devata
trishtup chandahah
shanaish-chara preety-arthe jape viniyogah
dasharatha uvacha
Om. Sri Shani Stotra, Dasharatha is the Rishi (seer of the mantra). Shanaishchara is God (related to this hymn). Trishtup is a metre. Enjoined is repetition (of this hymn) for the appeasement of Shanaishchara (Saturn).
kono-antaka roudra-yama-tha babhruh
krishnah shanih pingala manda sourih
nityam smrito yo harate cha peedam
tasmai namah shree ravi-nandanaya
Prostrations to Sri Ravinandana (Saturn), who when regularly remembered as (the ten names listed in the first and second line of this verse) steals away the suffering (misfortune of the devotee).
sura asurah kim purusha ragendra
gandharva vidyadhara panna-gash cha
peedyanti sarve vishama-stitena
tasmai namah shree ravi-nandanaya
Prostrations to Sri Ravinandana, by whose unfavorable position, gods, demons, celestial beings, celestial musicians, celestial masters of various wisdom-teachings and even celestial snakes succumb to sufferings.
nara narendra pashavo mrigendra
vanyas-cha ye keeta-patanga-bringah
peedyanti sarve vishama-stitena
tasmai namah shree ravi-nandanaya
Prostrations to Sri Ravinandana, whose unfavorable position brings agony to laymen, emperors, common animals, huge animals, forest creatures, insects, flies and humming bees (irrespective of their status).
desah-cha durgani vanani Yatra
sena-nivesah pura-pattnani
peedyanti sarve visham-stitena
tasmai namah shree ravi-nandanaya
Prostrations to Sri Ravinandana, whose unfavorable position brings about suffering to countries, citadels, forests, war-camps, houses, and cities.
tilairya-vair-masha gudanna danaih
iohena neelambara danato va
preenati mantrair-nijavasare cha
tasmai namah shree ravi-nandanaya
Prostrations to Sri Ravinandana, who is appeased by giving in charity things like sesame, paddy, black-gram, molasses, rice pudding, iron, blue cloth, etc., and by chanting mantras on his day (Saturday).
prayaga-koole Yamuna tate cha
sarasvati punya-jale guhayam
yo yoginam dhyana-gatopi sookshmas
tasmai namah shree ravi-nandanaya
Prostrations to Sri Ravinandana, who manifests in subtle form before the yogis who meditate on him at any holy bank of Prayag (confluence) of two rivers; Yamuna and Saraswati, or in a cave.
anya-pradeshat swagriham pravishtas
tadeeya-vare sa narah sukhe syat
grihad gato yo na punah prayati
tasmai namah sri ravi-nandanaya
Prostrations to Sri Ravinandana, who bestows happiness to a person when He enters His own house (constellation); (though) when He leaves the house, does not return for a long time.
srashta swayam-bhoor bhuvana trayasya
trata hareesho harate pinakee
ekas tridhah rig yajuh sama murtis
tasmai namah sri ravi-nandanaya
Prostrations to Sri Ravinandana, who is the creator of three worlds, who is the self-manifested being, who is Hari the protector and Pinakin (Siva, bearer of the three pointed spear or pinaka), the destroyer, all in one, as well as the embodiment of the three-fold Vedas; Rig, Yajus and Saman.
konasthah pingala babruh
krishno roudroantako yamah
sourih shanaish-charo manday
pippalandena sam stutah
Thus, Pippalada praises Thee (by chanting your ten names as contained in lines 1-3).
etani dasha-namani
pratar-uthaya yah pathet
shanaishchara-krita peeda
na kadachid bhavishyati
Harih Om
He who chants these ten names, getting up early in the morning, will never suffer from the pain caused by Saturn. Harih Om.
The following is the Dasaratha Shani Stotra from Padma Purana
Dhyaathwa Saraswatim Devim Gananatham Vinayakam.
Raja Dasharathah sthothram Saureridhamathakaroth.
Namo Neela mayukhaya Neelothpala nibhaya cha,
Namo Nirmaansa dehaaya Deergha shmashru jataaya cha,
Namo Vishaala nethraaya Shushkodhara bhayaanaka
Namah parushagathraya sthularomaaya Vai namah
Namo nithyam Kshudhaarthaaya Nithyathapthaya Vai namah
Namah Kaalaagni rupaaya Krthaanthaka namoshthuthe,
Nameste Kotaraakshaaya Durnireekshyaaya Vai namah
Namo Ghoraaya Raudraaya Bheeshanaaya Karaaline
Nameste Sarva bhakshaaya Valeemukha namosthuthe
Surya putra namestesthu bhaskare bhaya dhayaka
Adho-drushte namasthubhyam vapuhshyaama namosthuthe
Namo Manda-gathe thubhyam nisthrinshaaya namo namah
Thapasa dagdha-dehaya nithyam yogarathaya cha
Namesthe gyaana nethraya kashyapathmaja sunave
Thushto dadasi Vai raajyam rushto harasi Thathkshanaath
Devaasura manushyaashcha pasupakshisareesrpaah
Thvaya vilokithaah saure dainyamaashu Vrjanti cha
Brahmaa shakro yamashchaiva rishayah saptha-tharakaah
Rajya bhrashtaashcha t’e sarve thava drishtyaa vilokithaah
Deshaa nagara graamaa dweepashechai vaadrayasththaa
Raudra Dhrushtyaa t’u ye drushtaah kshayam gacchanti thath kshanaath
Prasaadam Kuru me saure varaartheham thavaashrithah
Saure kshamasvaaparaadham sarvabhutha hithaayacha