Hmmm... Assuming you're not pulling my leg, any ground coffee is fine, but my personal favourite is 'Rich Italian' by Taylors of Harrogate. I've heard it said that getting actual coffee beans and grinding them yourself immediately prior to brewing up gives you the best health benefits (Coffee is officially 'good for you'. Again.) But I think any coffee will give you the bronchodilatory effect if your asthmatic and getting a bit short breathed.
My two pennies worth - yes, coffee is a recognised broncho dilator but somewhat bizarrely you'd be best off drinking instant coffee of some description as opposed to freshly ground coffee as the instant will have a "manufactured" level of caffeine in it, the freshly ground will be much more variable.
Or keep some pro-plus in your preps.