Yes, yes they did. The Japanese tried to design numerous experimental rifles towards the end of the war. The most successful one was the Type 4 (Yon-shiki jidousyoujyuu) Rifle. It was essentially a copy of the M1 Garand, but chambered in the 7.7x58mm round that the Arisaka fired. This wasn't an optimal round for the rifle but it worked. The rifle was 4.14kg with a barrel length of 590mm and was capable of firing at 840m/s. It operated with 2x 5 round stripper magazines for a total capacity of 10 rounds. About 250 of these rifles were produced before the end of the war but none of them saw combat. If an invasion of the Japanese mainland was required however, the Type 4 would have surely been implemented. One of the surviving rifles is on display at the National Firearms Museum in Fairfax, Virginia.
Sources-
The Complete Encyclopedia of Guns. p. 435. ISBN 1-57215-441-1.
Walter, John (2006). Rifles of the World (3rd ed.). Iola, WI: Krause Publications. p. 146. ISBN 0-89689-241-7.
The Japanese did attempt to develop semi automatic rifles during and prior to WWII. The two I can think of off the top of my head are the Japanese Pederson rifle, which was based off of John Pederson's Pederson rifle, and the Type 4/5 rifle. John Pederson actually went to Japan and had a number of rifles designed and built in 6.5 Jap in the 1930s. The rifle really never went anywhere and was ultimately abandoned before the war began. The Type 4/5 saw design and production fairly late in the war (1944ish?) and it was mostly a copy of the M1 Garand, but chambered in 7.7 Jap and instead of using an en bloc clip, it fed from stripper clips into an internal box magazine.