We have Tinker Board 2S (64-bit) and Tinker Board S (32-bit).
For 2S, I installed Tinker Board 2 Debian 10 V2.0.0 and then tried to install ROS Noetic by following Debian instructions here. However, I came across a couple of issues including invalid key and unmet dependencies. Eventually, I was able to install ROS Noetic on 2S.
For S, it has 32-bit. So, as tfoote mentioned above, you need to build it from source. Here is the link for the ROS Noetic source installation.
I saw some people suggest using Armbian or Lubuntu on Tinker Board but there is no ready-to-use (e.g., with u-boot) Armbian or Lubuntu images for Tinker Board 2S. This means you need to prepare your operating system, for example Armbian, image by building it from source and adding u-boot. Otherwise, the device will not boot. On the other hand, there is Armbian image for Tinker Board S here. For our S model, I installed Armbian and then built ROS from source.
I'm using Nvidia TK1 which is a 32-bit cpu with Indigo on Ubuntu 14.04 32-bit. Seems to be working ok.