I work in Peds, not LTC, but we often have parents/family who say the same thing about their child.
If the family says the child needs something for pain, I will ask, "What makes you feel that way?" That gives them a chance to explain what they have observed (if anything) that makes them think the child is in pain. If the child was recently medicated, or has been showing no signs of pain, I'll usually suggest alternative methods first- holding, feeding, distraction, less stimuli, etc.
If it's an older child, I'll ask the child directly if they are hurting. If it's an infant, I'll sometimes explain the FLACC pain scale that we use to assess pain in infants so the parents can understand how we are judging if their child is in pain.
If the parent does NOT want a pain medication given, and I feel it's necessary, education is key. Explain that the dose of medication is an appropriate dose for the patient's pain. (If it's a lower dose, say that.) Explain that using a narcotic pain medication periodically or for a short period is not going to cause addiction. Explain the difference between tolerance and addiction. Believe it or not, we have many parents who don't want their fresh post-op, NPO child given IV morphine because they think they are going to end up addicted.
For an alert and oriented resident, just ask the resident directly if they need something for pain. Keep in mind that some older people do not feel comfortable expressing to the nurse that they need something. Many residents feel that they are burdening or bothering the nurse by pushing the call bell and requesting something for pain. Others may be used to the "tough it out" mentality with which they were raised. They may be more willing to verbalize pain to their family.
I try to remember that, before the patient came to the hospital, they were cared for at home by their family. The families often know the patient the best. In my job, this is often most true of children with chronic medical conditions who cannot communicate (such as CP with contractors.) This is also true of LTC residents. They have gotten to know how their loved one usually reacts and behaves, and what mannerisms they exhibit if they are uncomfortable.
If the resident is not able to communicate their needs, has a PRN order, and giving the medication will not cause harm, consider just giving the pain medication and chart "upon request of the POA/family." Pain can be difficult to assess in the elderly who cannot communicate. Normal age-related changes, arthritis, joint stiffness, being contracted, or even lying in bed for extended period can cause pain. Remember that sleeping or the appearance of sleep does not mean that the resident is not in pain- if the nervous system is overwhelmed by pain, it may just shut down. So at the very least you're making the family feel as though their loved one is being well cared for, and you may even be treating pain as well.