You now know what to look for to spot those particular types of replicas, but the only way to have confidence in telling fake from fair dinkum is to become very familiar with the genuine article. Lacking that, your best bet is to buy from a trustworthy source.
Just as the best place to buy genuine US coins is to buy from American sellers, the best place to buy Australian coins is from Australian sellers. If you want to go that route, you might want to try starting a thread in the "wanted to buy" section, with a link to this thread. Some of the Aussie members here might be happy to help you out (sorry, I don't have a spare one at the moment). 1937 crowns are typically trading at around AU$25 to $30 each here in Australia.
As for general tests of genuineness, I can only offer the usual list given for any type of coin: weight, magnet, specific gravity, edge, appearance. If they all match, then it's a reasonable chance the coin is genuine; while a fake coin can appear to match all of these, it just isn't worth the counterfeiter's while to do so for a coin with as little numismatic value as the '37 crown.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis