What do you mean by find? (at the coin shop, ebay, metal detecting, roll searching?) What do you mean by nice? (2012 pennies are nice) What do you mean by rare? (low mintage, old, error?) What do you mean by valuable? (more than face value, $100?)
Some I've found within 5 minutes. Some I've been trying to find for years. Some don't even exist, so I'll never be able to find them.
After I completed my set of Meiji 2 sen pieces except for one year, it took me nearly five years to find that missing example.
How long? It's been a while since I found a 42/1 Mercury dime in a pawn shop junk silver bin, but maybe I'm due. One can dream.
I am currently trying to complete a modern proof series, so widely available and mostly affordable. However, it's still taken me years. Also, there is one coin I need left, and I see new auctions for it all the time. In theory, I could just buy it and be done with it. However, I have taken it as a personal challenge to pay less than what I see them go for daily. I bid often, and so far have probably been the losing bidder on 50 auctions for this one coin. One day, I'll get that coin at the price I want, but it may take another few years.
How long? I really want to say something dirty. What is the coin Geekpryde? I promise not to run the bid up on you.
Well I got lucky once almost twenty five years ago, but who knows it can happen again. Study the key dates and varieties then go hunt. If nothing else, you can pick up some nice MS coins at about melt.