It's possible. The tricky part would be getting them all the same size, a shuffle-able size... basically, makeshift card stock doesn't tend to last for very long.
Then, even if you're a great illustrator, the sheer effort in 78 drawings might not exactly be worth it unless you go to an actual cardmaker and argh argh argh...
So, yes, playing cards might be one option. Lenormand, maybe?
What's stopping you from getting your own tarot deck? If you think you need to have it given and not bought, that's just a superstition. I bought my own deck and we work together really really well.