Is there a way to see how many coins you have of your daily limit?

There is no place to see it immediately (would be a good addition to the game though).

But, as @Wondercricket mentioned, you can count the coins you've earned today from Pokeball icon -> News -> Notifications. The Notifications include also recent friend related activity, so you might have to scroll it a bit down. Formerly they were seen in Journal, but the most recent update changed the location.

In a recent update, you can now see how many coins you accrued each day. The amount of accrued coins for a given day will appear on the “today”