4bt will fit, even without a lift
http://www.4btswaps.com/forum/showthread.php?120-4BT-in-a-Ford-Explorer...&highlight=explorer
The 4bt weighs roughly twice what the 4.0 OHV weighs
A b3.3 is easier to fit, and if you want, I can give you a link to a guys swap thread for that too.
You can find a 4bd1t for cheaper usually, and they are almost the same as a 4bt (size, weight, power, economy, tuning possibilities)
a mercedes om617 supposedly will fit without any modification(edit: after measuring, it seems one must relocate the radiator, and may need to cut the rad support just to get the engine set inside), and in the later models, like from the 83 300D for instance, they are only short about 25 HP from what the 4.0 makes stock, but they have slightly more torque, and run about the same revs as the 4.0 ohv. You can get more power out of those engines and they are nearly indestructible.... seriously, they outlast any vehicle they are put inside of. Just so you know.... a 4bt in stock trim out of an older bread truck is also usually tuned for around 130 horse....
If you are not Towing anything a VW 1.9 TDI will pull an explorer around too. If you tow.... well, watch your EGTs
Average cost of a swap if you don't have a combination of tremendous luck, a cheap or free engine, and more tools and fab equipment than most people can dream of..... 5000-10000. An engine and adapter plate on their own can run 2000-3000 for a used engine and around 1000 for the adapter plate/flywheel and all that noise. You can find 4bts with a ford bellhousing adapter already on them though, so that is one way to save money. All the little expenditures, hoses, clamps, wire can add up to $1000 or more in no time. Plus, there is more. The reason the average is so high is because most guys choose to rebuild the engines and make them run good before they go through all the work of putting them in the truck. (no sense spending all that money on an engine that might crap out on you in 6 months)
It is not cheap, and it will take you more than 10 years to recoup the money from the swap if you are looking to do this just for the fuel savings.
It is not easy to do by ANY stretch of the imagination. If you don't know diesels, or don't know what you are doing, stop now and learn more. When you do know what you are doing, expect to devote the better part of a year (some take longer) to the swap if you are just putting in a few hours and weekends here and there. They can be done in much less time, but generally, you need to be pretty damn well equipped and know what the heck you are doing. That and you need all the cash upfront to buy everything you need.
Like rhauf said earlier though, if you just want a diesel, buy something that is already diesel. It is cheaper and easier, and you can still easily get mid 20s to lower 30s for fuel economy out of even full size trucks. The ONLY reason to ever do a diesel swap in a vehicle is because you have a vehicle that you cannot justify separating yourself from. This is why most of the diesel swaps you hear about are on Jeeps. Guys love their jeeps, and they can't get anything like a jeep with a diesel. Explorers.... well to some people, they are the perfect vehicle.... but.... well, if you are just looking for a diesel vehicle, an explorer doesn't have a lot to offer.
Unless you are madly in love with your explorer, do NOT contemplate putting a diesel engine in it. You will just get frustrated and get rid of it.