I have had this discussion with my husband recently. It seems everywhere we go we need to go thru the "giant wall of buckets". It isn't a matter of giving, it's the manner in which I am asked (or demanded) to give. If it's a greeting with no expectation of a donation, I'm more likely to give the pocket change I have with me (I don't carry a lot of cash). If asked in a pushy manner, I have no desire to give any money to that person. I might give to the charity in another way, just not to the demanding person. That being said, even though the children were requesting donations to a charity, it doesn't sound like they are being taught the best way to act and react when someone says no. add to that the fact that the adult reinforced that behavior, I don't blame you for not wanting to make eye contact.
Perhaps a small smile with a shake of the head and a 'sorry, no.' as you are walking? (Maybe ask for a pamphlet about the charity or at least an short summary of what it's for/where the money goes. If the children are asking for money, they should have a good grasp about what the charity is about and what the money is used for. if they don't, they shouldn't be asking for money, IMO) If all else fails, you can pull out your phone and make a phone call, even if it's to your voicemail as a reminder what to pick up at the grocery store. Most people, even children, won't interupt you while you are on the phone. you can couple that with eye contact and a small shake of the head.