Address how Garrity and Gardner may apply to a police officer who you think may have child pornogaphy in his possession?
These two cases are relevant to the situation you describe only with regard to how the police officer may be treated by other police officers. This typically has to do with internal affairs investigations of police officers. In this case, what these two cases mean is that you will not be able to coerce the officer into waiving his right against self-incrimination simply by threatening him with the loss of his job.
What these two cases did was to clarify how personnel actions (discipline) against an officer relate to that officers right against self-incrimination. What the cases say is that a police officer may not be threatened with discipline in order to make them waive their right against self-incrimination. This means that you could not tell this officer that he would be fired (or otherwise punished) if he did not answer questions about the alleged child pornography. If you want to force the officer to answer questions about the child pornography, you have to give him immunity.
So, these two cases mean that you have to prove the case against this officer in some way that does not involve forcing him to answer questions under pain of being fired or otherwise disciplined.
Garrity applies to protection from self-incrimination for police officers. The officer is entitled to representation and cannot be threatened with dismissal or disciplinary action for not answering questions.
In Garrity v. New Jersey and Gardner v. Brodick the Fourth and Fifth Amendment protections are applied to police officers. Even though people sometimes want to hold them to a higher standard, police officers still have civil rights. Since they are police officers, there are opportunities for abuse in interrogation due to the fact that the person is a police officer.
If a police officer is found in possession of child pornography, he is committing a crime. Even the possession of this material is a crime. However, the officer cannot be threatened with dismissal from duty for not answering self-incriminating questions.