Upgrade to latest alpine which is now 3.10 and thus bind 9.14.3 - thanks to @ikluft for pointing this out. Also, it seems that Alpine 3.10 has removed rndc-config from the bind package, and it's now in bind-tools.

container/Dockerfile

@@ -1,7 +1,7 @@
 FROM alpine:latest
 EXPOSE 53 53/udp
 
-RUN apk --update upgrade && apk add bind
+RUN apk --update upgrade && apk add bind bind-tools
 
 # /etc/bind needs to be owned by root, group owned by "bind", and chmod 750
 # since we are mounting, do it manually
@@ -15,7 +15,7 @@ RUN apk --update upgrade && apk add bind
 RUN mkdir -m 0770 -p /etc/bind && chown -R root:named /etc/bind ; \
     mkdir -m 0770 -p /var/cache/bind && chown -R named:named /var/cache/bind ; \
     wget -q -O /etc/bind/bind.keys https://ftp.isc.org/isc/bind9/keys/9.11/bind.keys.v9_11 ; \
-    rndc-confgen -a -r /dev/urandom
+    rndc-confgen -a
 
 COPY configs/. /etc/bind/