You can also send for their Individual Deceased Personnel Files (IDPF). As others in this forum have addressed, the info found in an IDPF can be graphic. If you pursue this resource, you should be prepared for that possibility. Send your request to: US Total Army Personnel Command ATTN: TAPC-PAO (FOIA) 200 Stovall Street Alexandria, VA 22332-0404 Be sure to cite the Freedom of Information Act in your request. (This says ARMY, but they hold IDPF's for all branches for WWII.)
Depending upon the type of info you are seeking, you might try contacting a unit veteran's organization (re the cousin whose unit info you have).
On the other cousin, have you tried a search of stateside cemeteries?