They would later create a chibi version of the Kunio-Kun series popularized in America as the "River City Rampage", "River City Sports" and "Super Dodgeball" series
BUT...in the early 90's they made two beat-em-up games fro the SNES. There's been an argument as to whether these could be considered sequels and part of the River City Rampage series...or...Renegade?

Shodai Nekketsu Kouha Kunio-kun
1992/Super Famicom
Given it's not aesthetically at all like "Downtown Nekketsu", and is given a title to denote a continuation of Nekketsu Kouha Kunio-Kun, I'd say this right here is your first official sequel to Renegade.
Here's where it starts to get a bit...complicated

Shin Nekketsu Kouha Kunio-kun - Kunio Tachi No Banka
1994/Super Famicom
A lot of the characters from the first arcade Japanese version of Renegade are present here, however the characters have a more River City Random-ish look, and there's the RPG/dialogue elements from RCR/Downtown Nekketsu.
To me the REAL sequels to River City Rampage ARE:
Nekketsu Kakutou Densetsu - Famicom (1992)

River City Random Ex

Downtown Special - Kunio Kun no Jidaigeki Dayo Zenin Shuugou!

Nekketsu Kouha Kunio-Kun: Bangai Rantouhen(AKA Double Dragon 2 Game Boy...confusing, I know!)

(not included here are all the street challenge Kunio games nor the Dodge ball series)
article on the Kunio Kun/Renegade/River City Random/Dodge Ball/Sports series
http://www.hardcoregaming101.net/kunio/kunio.htm
AND, if things were not confusing enough...
We have the "American/Unofficial" sequels to Renegade from the late 1980's, made by
Target Renegade 1988

Target III 1989

(what the heckity heck is this game???)
Personally, I feel Target Renegade and ESPECIALLY "Target III" should be seen as how the Strider and Capcom community views "Strider Returns"...ie: it doesn't exist or count,
and Strider 2 is the real sequel to Strider 1. Though...many people and even critics praised Target Renegade, but is it officially a sequel?
Or is Shodai Nekketsu Kouha Kunio-kun the one true Renegade sequel?