Lord Sri Ram is regarded as the seventh incarnation of Lord Maha Vishnu. Lord Rama is one of the most popular gods in the Hindu religion and also the central character in the great epic Ramayana. The character of Ram is that of an ideal person. He is an ideal king, ideal son, ideal husband and an ideal brother. This Avatar of Lord Vishnu appears on Earth in the Treta Yuga and kills the demon Ravan who had received a boon from Lord Brahma. Diwali, the biggest festival of Hindus, is associated with the return of Srirama along with Lakshman and Sita after 14 years of exile. Rama nama in itself is a divine mantra and just chanting the name of Ram (Ra ma) helps one to attain salvation. The Mantra ‘Ra ma’ is called the Thaaraka mantra and is a combination of Namasivaya mantra and the Om Namo Narayanaya maha mantra thereby representing the merger of Shiva and Narayana. Another mantra of Rama is "Shri Ram, Jai Ram Jai Jai Ram". More mantras of this Deity are given below.

Rama Bija Mantra

Neelambhuj shyamalkomlang Sita Samaropitvambhagam

Pano Mahasaikacharoochapam

Namame Ramam Raghuvanshnatham.

Rama Healing Mantra

Om Apadamapa Hataram Dataram Sarva Sampadam
Loka Bhi Ramam Sri Rama Bhuyo Bhuyo Namamyaham

Rama Wish Fulfilling Mantra

Sri Ram Jaya Ram Kodhanda Ram

Rama Gayatri Mantra

Om Daserathaya Vidhmahe
Sita Vallabhaya Dheemahe
Thanno Rama Prachodayath.

However, Sri Agasthiar has given a set of much more effective Ram Siddha Mantras based on the days of the week where every day different mantras are chanted.

Monday - Sri Ram Jaya Ram Siva Ram
Tuesday - Sri Ram Jaya Ram Jaya Jaya Ram
Wednesday - Hari Rama Hari Rama Rama Rama Hari Hari
Thursday - Jaya Rama Siva Rama Guru Rama Jaya Ram
Friday - Sita Rama Hanumantha Rama Sita Hanumantha
Saturday - Sri Ram Jaya Ram Sundara Ram
Sunday - Sri Ram Jaya Ram Raghu Ram

See the Video below for more details.