You can just create your own XML or RSS file. For this answer I have used this example to build on. I also used Wikipedia for an example RSS feed.
filename: categoryname.rss
---layout: null---<?xml version="1.0" encoding="UTF-8" ?><rss version="2.0"><channel><title>{{ site.title }}</title><description>{{ site.description }}</description><link>{{ site.url }}</link><lastBuildDate>{{ site.time | date_to_rfc822 }}</lastBuildDate><pubDate>{{ site.time | date_to_rfc822 }}</pubDate><ttl>1800</ttl> {% for post in site.categories.categoryname %}<item><title>{{ post.title }}</title><description>{{ post.description }}</description><link>{{ post.url }}</link><guid isPermaLink="true">{{ site.url }}{{ post.url }}</guid><pubDate>{{ post.date | date_to_rfc822 }}</pubDate></item> {% endfor %}</channel></rss>
The title should be something like: 'mysitenames categoryname archive'. The description could be your category description. Link is the link to the category. The 'lastBuildDate' value could be the date of your last post and 'pubDate' could be the same.
Please let me know if you have any questions.