I take the 81mg enteric coated aspirin at bedtime and have had no troubles. Enteric coated, full strength aspirins may help, as epstns reported, but you should be careful with aspirin or other NSAIDs. Although its effects don't show up on INR testing, aspirin makes the platelets less 'sticky' and can cause more bleeding. If aspirin is irritating your stomach, and causes bleeding, and you take Warfarin, you could be looking at some issues with stomach bleeding that doesn't stop quickly.
Personally, I'd probably stay away from aspirin if it irritated my stomach.