Shri Ram and Mata Sita are the most famous couple from the epic. Besides them, original Valmiki Ramayana doesn't really deal with any other love story. Dashrath was very much in love with Kaikeyi but her evil boons made him forsake his love for her.
In Ananda Ramayana, Kusha and Champika are a marriage of royal convenience and Kusha and his second wife Kumudvati are a match of alliance but they develop natural love for each other. It's even mentioned in Raghuvansh.
Yupaketu (son of Shatrughna and Shrutkirti) had a love story of his own with Madansundari (Princess of Shivkantipuri) and he had Rakshasa Vivah with her.
Ravana and Mandodari are not a typical love story but when they first met when she was standing alongside with her father, he noticed her beauty and had a pure , ritually approved marriage with her and she was his Chief Queen. She was the only woman he truly respected being mother of his children and his favourite son Indrajit (Meghnad).
In Ananda Ramayana, Meghnad and Sulochana are an ideal couple who were very much in love with each other.
Devnadi Ganga and Shanthanu (Mahabhisha) fell in love with each other and got married but she left him when he broke his promise of never questioning her when she was saving vasus from curse.
Other lesser known couples are Yuddhisthir and Devika, Bhim and Valandhara, Nakul and Karenumati, Sahdev and Vijaya.