If the multivitamin with added iron suited you OK, why not go back to taking that? Most multivit+iron combinations contain about 15mg of iron, which most people's guts can handle (and which is enough to prevent, but not treat, anaemia if you're not losing a lot of blood from anywhere), whereas free-standing iron pills such as ferrous sulphate and ferrous fumarate have four or five times as much iron per tablet.
Extra fruit and veg and extra fluid are well worth a try, as is taking the iron tablet with meals. Make sure it isn't a slow release iron preparation, as the iron needs to be released high up in your gut to be absorbed, not in your colon where it will only make you constipated.
Red meat isn't the only source of iron - dried fruit, leafy green vegetables, poultry, breakfast cereals, chocolate (can't avoid the stuff today!), red wine and casseroles cooked in iron pots all contain useful amounts.
If all else fails and you do want to keep taking a high-dose iron supplement, try changing to a different brand. In theory it shouldn't make a difference, but in real life it often helps.
Cheers, V-rap.