Certificates for hosts on private networks

No I don’t think it’s possible. Regardless what CA you choose.

At first LE will not issue certs for IP addresses, see Certificate for Static IP.

Secondly it’s would not be possible to issue a cert for a local IP, because everyone could issue a cert for it’s own local IP. So everyone could get a cert and go to your network and intercept all HTTPS connections.
Additionally it’s not possible for a CA to prove you control a local server behind an IP. How could a CA access this server?

The only way to provide HTTPS for local IPs is to use self-singed certs, which will of course trigger error warnings.