You could just install BIND or any other DNS server on one of your droplets. Enable DNS caching to save on the amount of bandwidth that you use if that is an option for the server software you decide to use.

Then all you have to do is set your droplets up to use your own DNS server rather than Google's public DNS servers. You can (and should) set your server up so that it only responds to requests from your own droplets, and you can then choose not to limit the number of lookup requests your Minecraft server list software is allowed to make.

Of course, it is possible that there could be some advantage in Digital Ocean setting up their own DNS servers for use by the droplets in the local datacenter, if just in the bandwidth savings thanks to caching, but if they don't decide to set up DNS servers for use by the droplets in each datacenter, this would be a way for you to get around the limits placed on you by Google.

In fact you can go even simpler.

Just install your favourite resolver (bind, unbound, pdns-resover, etc) on each droplet, have it listen(2) to 127.0.0.1:53 and put »nameserver 127.0.0.1« as the first line in resolv.conf.

(The debian and ubuntu packages for unbound, as one example, default to listen(2)ing only on 127.0.0.1:53.)

Even a 512 is large enough to run its own caching, resolving (and preferably verifying) name server.

Unfortunately at this time we aren't looking into this feature but you can setup two small droplets and run DNS services and it should resolve the issue you are having with requests since a single DNS server can handle quite a significant load.

Thanks