Please be aware Atlassian doesn't do "stable" versions. They do it the right way - they simply release, not bugger around with pointlessly noisy arbitrary releases. (And, yes, they do early access stuff, but you have to volunteer for that)
The EOL date for Confluence 6.2.x is May 15, 2019. Please see: Atlassian Support End of Life Policy for more details.
The latest version is Confluence 6.6.1, a bug fix release so it should be stable. It will be EOL Dec 12, 2019. Here are the bug fix notes: Issues resolved in 6.6.1
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