Sounds possible with BIP-32. Generate a seed private key and give its xpub to a miner. The miner can computes as many public key as it wants by bruteforcing non-hardened derivation paths, and once it finds one that matches your criteria, it replies with the derivation path. Only you can compute the private key with the seed private key and the derivation path.
Throw away the seed once you're done, don't reuse, otherwise the miner might correlate your npubs.