Can i use aternos for my coop speedruns and other third party server hosts?

The rules say

The entirety of the run (from time start to end) must be done on a external server or while Open to LAN

So I guess you can indeed use aternos for your coop speedruns

Yes, you can use Aternos for your co-op speedruns in Minecraft. According to speedrun rules, the entire run must be conducted on an external server or via "Open to LAN." However, some users report that Aternos servers might not be ideal for speedruns due to potential latency issues.

It is recommended to test the server's performance in advance to ensure it meets your needs.

For guidance on setting up a private server on Aternos, you can watch this tutorial: Minecraft: How to Create a Private Server on Aternos.