This was one of the big original Hawaiian makers of mass produced Ukuleles. They were in business from 1918 to 1935. They were the first ones who put the Aloha with the Hawaiian royal crest on the headstock of Ukuleles. They sometimes put a K' in front to make K'Aloha and a lot of them had the Akai embossed in the sound hole too, (Tai Chong Goo who was the head luthier and worked under the pseudonym Akai). When the company folded, Tai continued making Ukuleles on his own under the name Akai Ukulele & Curio Company; he died in Honolulu in 1968 

As well as the Aloha Ukuleles they also made a brand called Paradise of the Pacific with a much more US centric headstock decal. With this name meant it may have been connected with the long running Hawaiian magazine "Paradise of the Pacific" (Founded by royal charter in 1888 and still going today but it changed its name to Honolulu magazine in 1966)? Alternatively I have read that this brand was sold specifically by the Island Curio Company, (founded 1900). 

Another Brand associated with them is Lanai. Quite what the relationship was I don't know and though some of the Lanai ukuleles are unmarked beyond the Lanai sound hole label, they were clearly made by the Aloha Mfg Co. and I have seen examples that did have the Aloha logo on the headstock too. Possibly this was another Hawaiian shop that was re branding them?  

Over the years a lot of people have put Aloha, (as it is a common greeting in the Hawaiian language), on the headstock of their Ukulele and it continues today with a number of cheap imports to Hawaii for tourists All of these are nothing to do with this firm.