First of all, let me say that it's really great to see folks thinking about their parents and wanting to take care of them (monetary or otherwise) in their older years - it's uncommon these days in the generation of ungrateful children (I know many kids who would and do simply put their parents in a home or just leave them to fend for themselves), so it's always nice to see. Anyhow, just curious - do they know you are doing this for them? Reason I ask is that if they do know, it would help you in making the decision on how to get them the money if you find out from them their preference. If you don't know, would you have a sense of how they usually pay for things? For my parents, they would use a credit card over a debit card and cash, but use cash more than a debit card. Also, you may want to find out whether they have easy access to their bank branch or an associated bank ATM (in Canada, we only have 5 major banks) - this also depends if they use an ATM or not - if they are the type to go to the teller, they may face long line-ups; if it's not nearby, perhaps you can wire them money through Western Union or something like that. Sending a cheque may not be the best idea, since they have to remember to cash it, find time to cash it, and travel to their bank to cash it (and if they don't deposit using ATM, they may face a lineup).
I like your credit card idea. If you find a credit card that also has rewards/points, then you can be helping your parents, but also accumulate points for groceries or gas or whatever.
In Canada, at several of the gas stations, they offer this "quick pay" type of device like a keyfob or someting like that, that can be swiped at the pump - it's pre-paid and pre-filled so it's nice and easy. I suppose you can probably set something up like that, if it's available, so that you pay for a pre-charged amount of gas and the gas station company issues them the fob or device every month. They don't have to worry about cash, but instead simply swipe and fill up.
As for the tax stuff, I'll leave that to someone here who is knowledgeable about tax laws and such.
My parents are not collectively retired just yet (my Dad is, but my Mom is still working till she turns 65 in a couple of years), but I've been thinking of the same things you have been. It's a good way for me to show my appreciation for all they've done for me, in a tangible way, even though I know I can never fully repay them for all the headache I've caused them when I was a kid...
A set of my cousins has an interesting arrangement, but it's far different than what you and I are talking about here. My uncle, who seems to be a hoarder of anything monetary, charges them a "child fee" every month, which they gladly pay. My uncle's premise behind this is that children should be helping out their parents (which I agree with), but he took the extra step in taking the initiative to start billing them early. Seems kind of weird to me as an ask, but my cousins don't complain and gladly oblige. It's almost like paying parental reparations, an existence tax, or something like that...
You are a good person and have my respect. I know in many Asian cultures it's customary if not expected for children to help their parents in their old age. I hate to bring in the "American culture has corrupted traditions" argument, but I do think to some extent American culture has indeed taken that sense of responsibility and obiligation away from many Asians.
