Well, 'When We Were Kings' can be considered in a way. It's mainly about the famous boxing match but also shows the love and admiration in the community. 'I Am Not Your Negro' isn't strictly a love story documentary but it does touch on the love for a community and the struggle for equality which has undertones of love. And 'Searching for Sugar Man' has a story of a musician's rediscovery which is intertwined with the love his fans had for his music.
There's 'The Salt of the Earth', which chronicles the life of Sebastião Salgado. His work and his relationship with the world can be seen as a form of love story. 'Amy' is also a documentary that has elements of love, as it shows the life of Amy Winehouse, including her relationships and the love that her fans had for her music, as well as the complex love she had in her personal life.