In my opinion, in the original manga it's implicit that both Tenshinhan and Piccolo learned Kaioken from Kaio-Sama.
In
chapter 312, Tenshinhan says that Goku will win against Freeza because of Kaioken:
"Don't worry. Goku will win. Have you forgot about Kaioken? With this level of trainment, he must be capable to use Kaioken x10" (And then Kaio-Sama replied that Goku was already fighting with Kaioken x10)
In the manga we see nothing about what kind of trainment Tenshinhan, Yamcha, Chaozu and Piccolo received from Kaio-Sama, but it's suposed it was the same kind Goku received. And learning the Kaioken is the most crucial part of it. Of course, it's very difficult to learn this technique, and so I don't think Yamcha and Chaozu managed to do it. But Tenshinhan and Piccolo are genius fighters almost as much as Goku is.
In the quote above, we see that Tenshinhan didn't just know Kaioken, but he understood it to the point as to be certain Goku would be able to use it x10.
In
chapter 314, when Kurilin told Piccolo about the Genki Dama, he said:
"Damn Kaio... He never told me nothing about it"
Piccolo didn't made a similar comment about Kaioken before. So, it's clear to me that Kaio-Sama mantained just Genki-Dama as a secret, but teached Kaioken to Piccolo and Tenshinhan.
This also explains why Piccolo was stronger than Android 20 in the Androids Saga. And also Tenshinhan being capable of stopping Cell for a while and achieving the completely outstanding feature of repelling a blast from Super Buu (Gotenks absorbed) with Kikoho.
So, why it's never shown Piccolo and Tenshinhan using Kaioken?
Well, Goku used Kaioken x10 against Freeza and was never shown he expliciting saiying "Kaioken", until that Kame Hame Ha x20 Kaioken.
As Dragon Ball arcs passed, some important techniques just stopped to be mentioned, despite the fact that a lot of characters were using them all the time. That happened to Zanzoken, Bukujutsu, Chou Kame Hame Ha (just being mentioned simply as "Kame Hame Ha" in arcs after the 23rd Budokai Tenkaichi). And I believe that also happened to Kaioken from Freeza's fight onwards.