Is there any cryptonote coin that has a working mobile wallet?
Try monerujo for monero (XMR).
monerujo for Android
or CAKE for iOS11.
are the best True Wallets,
there are other that are Web Wallets with an App, that do Not have/give Private Keys.
Anyway...
CriptoNight/CriptoNote wallets work different than Bitcoin, Ethereum wallets, like: Exodus, Jaxx, Coinomi, Copay, etc...
A Node = A Complete Wallet, for Bitcoin or Ethereum is over >200GB,
a Mobile Wallet, must trust a Node.
but XMR, BCN are different...
A XMR Node was less than 50GB,
a BCN Node is around 20GB, today.
Wallet must search All the Blocks in the Blockchain from date 00000 for the Address You have, and store the Search Results in the Phone, usually around 50MB size: 0.01%
Does Not Trust, Needs to Search...
to search you must give a valid Node Wallet Address.
you can download a complete Node in your PC, and give that IP address to your Phone, your Phone will search all the blocks, takes a few hours, downloading the Full Node wallet takes much more time.
or you can give another Known & Trusted Node Wallet address IP.
Usually All Pools have a Trusted Node Wallet, for example:
node.supportxmr.com:18081
in monerujo you can have different/multiple Address,
but you must Search / Sync / Scan Each address individually.
when Scanning/Sync is done, the App stores the result in the Phone, and Next time you open the Wallet, Monerujo or CAKE, will take less time to Scan / sync / search the blocks remaining "days behind",
Does Not Start Scanning From 0, unless you erase the Result Files or close the App without finish Scanning, time to sync 1 week behind is maybe a minute.
12:51
33,000 Blocks remaining.
1:08
Synced: 1,576,687
= 17 Minutes to Scan 30K Blocks.
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Jaxx is a Multi coin wallet, "BTC, BCH, BCG, Doge, ETH, ETC, etc.."
and tried to Add XMR / CriptoNight Wallet support, but they failed, because the technology is very different.
don´t hope too much for Multi-Wallets to Support CriptoNight coins.