Yoshi colors.

The word 'make' really isn't appropriate for this situation. For each different game you play, you get a different colored yoshi. That is the only way you can change the yoshi's color.

I've heard that you can also name your profile name something of the color you want. For ex. Snow=white and fire=orange.You can be red, blue, white, black, orange,and pink.

K save before you fight the harriers run away from them then get your yoshi if you don't like the color then restart you console the repeat un till you get your favourite color

According to mariowiki the color is determined by the time you spend with the egg. From when you rescue it on top of the Hot Dog stand to returning from the fight with the Armored Harriers.
0-6 minutes GREEN
6-9 minutes RED
9-11 minutes BLUE
11-15 minutes ORANGE
15-18 minutes PINK
18-19 minutes BLACK
19-20 minutes WHITE
*PS.: If it goes over 20 minutes the cycle restarts

As soon as you get a yoshi egg there's like a time limit 20mins if it goes over it restart. The color has nothing to do with the beginning of the game (when you choose the file n name) it's not true because I had a red file n I got a blue yoshi my files name was melody. Just go on YouTube if you need someone to show you how to get a certain color

Green 0-6 min
Red 6-9 min
Blue 9-11 min
Orange 11-15 min
Pink 15-18 min
Black 18-19 min
White 19-19 min and 30 seconds
If the time passes more than 19 min and 30 seconds then the whole cycle restarts