Simply use dnf

Copydnf -y install gcc-toolset-9-gcc gcc-toolset-9-gcc-c++
source /opt/rh/gcc-toolset-9/enable

ref: https://centos.pkgs.org/8/centos-appstream-x86_64/gcc-toolset-9-gcc-9.1.1-2.4.el8.x86_64.rpm.html

Note: source won't work inside a Dockerfile so prefer to use:

CopyENV PATH=/opt/rh/gcc-toolset-9/root/usr/bin:$PATH

or better

CopyRUN dnf -y install gcc-toolset-9-gcc gcc-toolset-9-gcc-c++

RUN echo "source /opt/rh/gcc-toolset-9/enable" >> /etc/bashrc
SHELL ["/bin/bash", "--login", "-c"]
RUN gcc --version

I am using CentOS 7.9 and I encountered the same problem after following instructions here to install and run gcc 11. I tried launching different versions of gcc and found only devtoolset-9 works, which corresponds to the file devtoolset-9 in /etc/scl/conf/ folder. So I copied devtoolset-9 to devtoolset-11 in the same folder, and gcc 11 gets working.

What I have so far:

cat Dockerfile

FROM centos:7 AS env

RUN yum update -y
RUN yum install -y centos-release-scl
RUN yum install -y devtoolset-9

RUN echo "source /opt/rh/devtoolset-9/enable" >> /etc/bashrc
SHELL ["/bin/bash", "--login", "-c"]
RUN gcc --version

So you must:

1. Add the source stuff in a bashrc
   note: On Centos it's /etc/bashrc while on ubuntu it's /etc/bash.bashrc

2. Update the docker default shell to be bash AND to "load" the bashrc using --login

Output

docker build .
Sending build context to Docker daemon  4.096kB
Step 1/32 : FROM centos:7 AS env
 ---> 8652b9f0cb4c
Step 2/32 : RUN yum update -y
 ---> Using cache
 ---> a2bb269cd8dc
Step 3/32 : RUN yum install -y centos-release-scl
 ---> Using cache
 ---> 1184e26c71cf
Step 4/32 : RUN yum install -y devtoolset-9
 ---> Using cache
 ---> e678665d2a4e
Step 5/32 : RUN echo "source /opt/rh/devtoolset-9/enable" >> /etc/bashrc
 ---> Using cache
 ---> fe1745d4ca87
Step 6/32 : SHELL ["/bin/bash", "--login", "-c"]
 ---> Running in 2dd7955f4487
Removing intermediate container 2dd7955f4487
 ---> 3cf4835bf680
Step 7/32 : RUN gcc --version
 ---> Running in b5de3266d607
gcc (GCC) 9.3.1 20200408 (Red Hat 9.3.1-2)
Copyright (C) 2019 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 ...

What won't work

Test 1

RUN scl enable devtoolset-9 bash
RUN gcc --version | head -1

each RUN is a new shell so the sub-bash is lost on the second line.

Test 2

RUN source /opt/rh/devtoolset-9/enable && gcc --version | head -1
RUN gcc --version | head -1

Here again the source is only for the first RUN shell command but will be lost...

Test 3

This may work but with potential unexpected behaviour

ENV PATH=/opt/rh/devtoolset-9/root/bin:$PATH
RUN gcc --version | head -1

here we only "fix" the PATH variable but if you look at the /opt/rh/devtoolset-9/enable script there is so more to do than only updating the PATH...