Kaitou Tantei Yamaneko- your best bet, butsomeone else recommended it to me so...
Medical Examiner Dr Qin- kind of like a good colleague friendship between two guys and girl, no love triangle or romance, but its vaguely hinted that the lead may love the girl, no romance or moments included though.
I think there is good bromance in School 2013, although your heart may be broken, don't think its very funny but romantic narrative was dropped so may again be hints, but no relationship... don't know much though
Bad Guys- on my To Watch might have good bromance.
Kisarazu Cat's Eye- supposed to be funny and again might have good bromance.
Honestly, I've only watched the second one, and there's no 'bromance' per say, mainly a good friendship. The first and third, people say has good bromance. The last two funny, not sure about bromance, but I think it has good male friendships in it so...
I'm sorry I don't watch Japanese dramas, and am a kind of romance-junkie so don't know what to recommend, but i gave it a shot.