Honestly, there are sometimes you can't make people happy. Sometimes it's other frustrations they have (work, relationships, money, etc.) that are really the problem, but you are who they interact with more and your job is (to some degree) to listen to there complaints, and well there it is. Sometimes people are just angry and not personable. Remember all those personality disorders you learned about in psych... well parents can have them. I don't think this is all that common, but it does happen. Sometimes parents are just so frusterated that their child is sick (generally kids with chronic illnesses in my opinion) that it is overwhelming for them (usually also related to work, money, relationship concerns) that they will seem oppositional. And lastly, sometimes there is a cultural reason (ie, they come from a gender dominated culture and if your the opposition gender, that can create hierarchy issues... also somewhat rare in my experience). But mainly, I think work, money, relationship (ie lack of parental support) stresses on top of their children being ill makes people really worried, which comes across as anger.
There really is nothing special to do per se. Just be professional and kind. Explain everything that is going on and everything you are planning to do for their children. Ask how they (the parent) are doing and if there is any other assistant you can provide (ie do they need to see a social worker because they don't have food at home or the parent just lost her job and medical insurance). And always symphatize with their frusterations like it sounds you were doing... "I sense you are frusterated, I know this must be hard for you and (insert child's name). If there is anything else I am able to do for you, please don't hesistate to ask." or something along those lines. I would try to avoid making excuses or somehow bringing yourself into their frustration like "I'm trying my best" because a) it puts the conversation on you when they are ones who are frusteration and b) allows them an oppportunity to get more frusterated at you... eg "Are you really doing your best?!" While you probably are, you can see how you being on the defensive makes the conversation go south quickly. In other words, sympathize and keep the conversation on them and their children. Leave yourself out of it.
Anyway, I hope that helps and even though it seems discouraging when a parent is angry at you, just remember that they really aren't mad at you typically, they are mad at their situtation and you are just there while they're on their soapbox.