The common way to say 'tell me a story' in Japanese is 銆岀銇亰瑭便倰銇椼仸銇忋仩銇曘亜銆 (Watashi ni o-hanashi o shite kudasai). This is a polite and commonly used phrase.
In Japanese, 'love story' is typically expressed as '鎭嬫剾銇┍ (ren'ai no hanashi)'. Different contexts might call for slight variations, but these are common ways to say it.