Install node and npm with nvm using Docker.

build.sh

#!/usr/bin/env bash

# confirm docker daemon is running and connected
docker version

# build the image based on the Dockerfile and name it `nvm`
docker build -t nvm .

# confirm image is present
docker images

# enter container terminal
docker run -it nvm bash

Dockerfile

# set the base image to Debian
# https://hub.docker.com/_/debian/
FROM debian:latest

# replace shell with bash so we can source files
RUN rm /bin/sh && ln -s /bin/bash /bin/sh

# update the repository sources list
# and install dependencies
RUN apt-get update \
    && apt-get install -y curl \
    && apt-get -y autoclean

# nvm environment variables
ENV NVM_DIR /usr/local/nvm
ENV NODE_VERSION 4.4.7

# install nvm
# https://github.com/creationix/nvm#install-script
RUN curl --silent -o- https://raw.githubusercontent.com/creationix/nvm/v0.31.2/install.sh | bash

# install node and npm
RUN source $NVM_DIR/nvm.sh \
    && nvm install $NODE_VERSION \
    && nvm alias default $NODE_VERSION \
    && nvm use default

# add node and npm to path so the commands are available
ENV NODE_PATH $NVM_DIR/v$NODE_VERSION/lib/node_modules
ENV PATH $NVM_DIR/versions/node/v$NODE_VERSION/bin:$PATH

# confirm installation
RUN node -v
RUN npm -v

You can add the nvm to your docker-entrypoint.sh file. This will make nvm/npm work in any login, even /bin/sh. The exception is when using the image in a multi-stage build. See below.

. "$NVM_DIR/nvm.sh"
exec "$@" # Last line

Include it like:

COPY docker-entrypoint.sh .
ENTRYPOINT [ "/docker-entrypoint.sh" ]

Images setup with NVM that are used in a multi-stage build require nvm to be setup manually.

FROM some_nvm_image

RUN \. "$NVM_DIR/nvm.sh" \
    && npm --version \
    && node --version

But don't put a lot of time on such problems. NVM is a localdev tool. If you're building for production, either use an official node docker image, or borrow their Dockerfile to build your own.