Tsk tsk the kids these days and their crazy dreams
Let me set you all straight as I've been playing Pokemon since Pokemon Blue and Yoshi was available back then. If Yoshi isn't good for you whipper snappers then tough but for the rest of you here is the code it still works in the newer versions and may take more than one try but trust me you'll get Yoshi in no time just keep at it.
1.Have a red and blue version and both players must have all 150 Pokemon. Trade a Dratini from the red version to the blue version 2.Have the blue version evolve it into a its next stage. 3.Trade it back to the red version. 4.Now go to the dungeon where you found Mewtwo and surf nearest to where you found him. 5.Use a Fire Stone on the evolved Dratini, it will say not available but you can use it anyways. Then it will start to evolve into Yoshi. It's moves will be the same as they were before but its ID will be 999.
Bam a Yoshi there's even a trick to catch a black yoshi as well and once you get that I'll show you how to catch Mew. http://www.psypokes.com/rby/mew.php
Also I think your supposed to flip your system upside down for the Yoshi at some point