Are there coins which you could mine with CPU so that it would be profitable?
The best one right now is Monero (XMR), it is on the CryptoNight algoritm, which is designed for the CPU mining, also there is a lot of other coins that you can mine, which are not so profitable right now, but the best way is to mine Monero, and if you want some other coin to have just buy it on exchange from the income.