Yawara!

A romance with obstacles was a very common theme in the '80s and these two anime are examples of such. In Yawara it's a romance between a judo prodigy girl Yawara and a third-rated sport news reporter Matsuda. In Maison Ikkoku it's between Godai, a tenant at Maison Ikkoku, and Kyoko, the new manager. In both anime the romance progresses nicely, but with way too many obstacles. 

I second this recommendation. For those Maison Ikkoku fans, don't be fooled by the appearance of Yawara!, it is actually more of a romance drama than sports. Judo is mainly used to drive the plot forward, but Judo competition itself is never a focus of the story. Both series involve seinen romance (the later part of Yawara!) between multiple people and there are multiple love triangles. More importantly, there are lots of difficulties involved in the primary romance; thus, it took the entirety of both series for the romance to blossom in the grand finale (7 years in the settings of the original mangas). (PS: for Yawara! you even have to watch the movie for that to happen). read more 

Both anime feature a female martial arts expert being trained by their grandpa, both of whom are short in stature, and a little bit perverted. The main character in each show is also reluctantly entered into martial arts tournaments by said grandpa. Both series also feature a reporter for a sports tabloid which wants to get a scoop on the main character. The art style and tone of each show are slightly different, but I feel like it's impossible to ignore the otherwise large similarities between the two. 

The fate between the two lies on how they be able to reach for it's certain dreams. Either does have a same similarities and concept for what makes sport become a huge inspiration that aspire more than flaws along with the realistic aspects of romance.