I'm really glad to live in such a friendly area. I've been hunting now for 2.5 years (probably 800-1000 hours a year), and I've had a whopping 2-3 encounters with irritable adults, and never in a tot-lot!
I'm pretty friendly if kids come up, but only AFTER I look up and look around to make eye contact with a parent. I can usually tell which parent belongs to which kid, because they're watching the kid engage with me. Once I find a parent, I nod and smile, and then start talking to the kid.
If there's no parent/adult who I can find connected to the kids, I simply ask the kids one of two questions,
1) Are you allowed to talk to strangers? (and that usually sends them scampering).
2) Where is your parent (and that allows me to make eye contact or at least monitor where they are).
The exception is if they come up in a group 3-4 kids in a group, and I simply start answering questions and giving instructions, like "I need you all to stay back... further... further... YES, that's how far..."
Only if there's a single group of kids on a playground with a parent keyed in on what's going on, will I give them anything I find. yesterday, a mom with 3 kids was at a tot-lot I was detecting, and I gave each of them a few coins, a turtle pendant (costume), and at the end of it all, I called the little girl over (mom was watching and waving) to come get a kids ring I'd just pulled.
At the end of it all, the Mom wished me well, told me to have a good day, and we waved goodbye.
I think, those kinds of interactions are what make it possible for the NEXT MDer to have fewer problems with parents.
The key, though is to be obvious in your actions. either be obvious in your ignoring the kids (which I've done, and works very well.. parents quickly see you're not engaging with kids at all), or be obvious in your engagement. And when parents hear you say stuff like, "Are you allowed to talk to strangers," oddly, it's a quickly reassuring thing.
And never... ever... touch them. Though... I did have one grandmother bring a 5 year old over who wanted to say something to me. The grandmother watched with a big grin as the little girl came over gave me a big hug and said, "Thank you Mister, for cleaning up our park." It was SO FREAKING ADORABLE.... I gave her a handful of quarters. LOL Here eyes lit up like fireworks.
I've been doing the parks often enough, too, that the regulars (including the park volunteers, whom I know by name, now.) know me, and wave when I show up. It's nice.
Cheers!