I don't know of any coins that you can invest with $2 or less for the long term. Doesn't make sensee, considering that transaction fees of moving the coins around exchanges and wallets will result in probably at least 10% of your investment lost.

But if you mean coins under $2 in value instead, I think IOTA is a good long term hold. Right now its value is under $1.5, which is extremely undervalued in my opinion. Once they add anonymity to their network and fix existing issues like disappearing balances etc., its value will skyrocket.

Also, Monero is a good buy as well. Obviously its value is over $100 per XMR but you can always buy fractions of a XMR. I'm holding XMR long term myself.