I try talking to them everyday and do tasks if they give me any to make a friendship. But it seems that Rod/Amelia/Marina continuously ping me. Is there anything I can specifically do to get them to ping?
I don't think there's anything you can do to get villagers to ping you. I've researched this obsessively over the past few days, some people suggest that you ignore them and they'll ping you, others say it's villagers you're very friendly with who will ping you. My own opinion is that it's somewhat random, the characters who've pinged me most have been characters I didn't completely ignore and chatted with but didn't overdo it.
The method of going diving for maybe 3 to 5 minutes seems to work. There was a rumor that Chester was leaving so that same day I went diving and he pinged. That gave me the chance to stop him. That was also my second ping for the day.
Don't ignore them either. Just treat them like regular villagers.