Upgrading curl on centos 6: libcurl-7.50 requires libnghttp2

You're using the third party city-fan repository. This repo has dependencies which are in the EPEL repository, one of which is libnghttp2, so you must have EPEL enabled to use city-fan.

Here is the complete set of commands I executed because it was not clear from the answer of Michael Hampton. Also the link to EPEL install instruction as pointed out were long and unecessary.

yum install epel-release -y
rpm -Uvh http://www.city-fan.org/ftp/contrib/yum-repo/rhel6/x86_64/city-fan.org-release-1-13.rhel6.noarch.rpm
yum update curl

Updated URL 2020-08-19: http://www.city-fan.org/ftp/contrib/yum-repo/rhel6/x86_64/city-fan.org-release-2-1.rhel6.noarch.rpm