There are two programs I have found for this so far.
This site allows you to use a program to recreate your mapmaker maps in blueprint form. This allows people to use the blueprints to recreate your maps in mapmaker. They have a database with tons of these blueprints. This is also cool, because people who created maps on gc and xbox can now share them with ps2 users and vice versa.
Also, another potential method exists to trade mapmaker data. A Playstation 2 memory card adapter could be used to transfer PS2 Timesplitter Future Perfect map saves to the PS3. Then the PS3 file could be traded over the internet. I myself tried this with someone, but could not get it to work. Although, I would have to test this out a lot more to figure out if it really will work or not.
There is also a way to exchange maps through the LAN tunneling program Xlink Kai. After playing a mapmaker map through Xlink Kai, if you exit out of the online portion of the game and go straight to your mapmaker. Then go into "Edit/Create New Map..". The map you just played should be loaded into mapmaker. Then you just hit save and it will save to your memory card. I have done it myself many times.
This method will always work eventually, but its a bit buggy. Sometimes when you go into mapmaker and try to save the new map the game will just totally freeze up. Sometimes the game will semi-freeze, the cursor moves but the mapmaker menu will no longer appear. If this happens, just reset your PS2 and have the other guy host the mapmaker map and try again. Eventually you will be able to get it to work.
After trying this many times, it appears as if there is a method to make this work much more frequently. When I didn't do this, the game would freeze most times when I tried saving the maps. When I applied the following method it worked 4-5 times in a row. Maybe there are other factors that contributed to it working better, but it did seem as if doing this significantly improved the chance of saving the map successfully.
Once you have gone into the mapmaker, then selected "Edit/Create New Map.." The screen will say "loading models please wait". As soon as the message disappears, press the Triangle button once to take away the menu, then use the analog stick to quickly scroll up to the top right of the screen as far as you can go. Sometimes it seems like after you press Triangle and hold the left analog stick the screen will hang for a second and not move. If that happens just continue to hold the left analog stick to the up and right and after a second or 2 it should let you scroll to the top right of the screen. Once you do that press the Start button on the controller. Then go down and pick "Save Map" and save it to your memory card.
Also. This method only works to transfer multiplayer mapmaker maps since that is all you are allowed to host in the LAN mode of the game.
I have heard about some devices like codbreaker or action reaplay and how they can move PS2 memory card data to the PC, so you probably could exchange map data this way as well. I don't have these devices so I cannot comment on that really.
They probably do work, but not many people have them so really would not be able to exchange maps with that many people.
Also, I know there are probably other methods out there that I do not yet know about, so if you know any let me know!
My goal is too eventually get every possible method listed here, so people will not have to go through what I am going through to find all of them. Google does not like to cooperate when searching for this type of stuff, as it seems to only find reviews from gaming sites.
Yea well, it still is way better than having to reconstruct the map from a blueprint.
Well I only tried it once, like usually the second time you try it, it will work. I just go lazy and wanted to continue playing haha.
That must be why you called lazy, you hobo!
After doing some experimenting tonight, it seems like I have found a way to make saving maps through Xlink Kai work more often. Thank you Slacker and GasHM for being patient while I tested it out for a long time heh. I updated the post with the new method.