You will need AWS's new modularized assemblies.
AWSSKD.Core v3 & AWSSDK.Cloudfront will do the work.
First you need to get the current Distribution mostly for validation you'll need to grab the Etag and Caller Reference. Etag to var and Caller Reference to string.
var client2 = new AmazonCloudFrontClient();
var tag = client2.GetDistributionConfig(new GetDistributionConfigRequest
{
Id = "YOURDISTID"
}).ETag;
string cf = client2.GetDistributionConfig(new GetDistributionConfigRequest
{
Id = "YOURDISTID"
}).DistributionConfig.CallerReference;
client2.Dispose();
Next you will need to make a update to the distribution. What I have below is the minimally required to update a distribution (Pretty much Everything you see in the AWS console when editing a distribution.