There may not be an easy/automated way to generate non-standard size key certs and the required CSR. But it is indeed possible and should be accepted by any CA. Given the key size is within the CA imposed limits: Generally 2048-4096
Here is just such an example:
An LE public cert for an RSA 3456 bit key
-----BEGIN CERTIFICATE-----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-----END CERTIFICATE-----