Coffee in itself isnt really acidic. People refer to it as "acidic" but really its not like its orange juice etc. Id be interested to know the exact pH, but according to my 5 minutes of Google reasearch, it seems like its more neutral than acidic, and varies from bean to bean (dry processed beans being lower in acidity, and darker roasts being lower in acidity).
You can buy drip coffee machines from Target etc, and from memory they are only about $30.
Now, for the stomach issue....I doubt it would be an issue directly with the coffee, but could be the caffeine itself. Have you tried decaf?? Just make sure its swiss water process decaf (ie no chemical decaffeination) and it should be fine. If thats the case then you could roast it yourself from Beanbay, or buy 1kg bags for $42.