If you're playing at Medium difficulty, then you are definitely doing something wrong.
In my two campaigns, I'm litterally drowning in Denarii (more than 500 000 when playing Julii and discovering the game, more than 2 500 000 when playing Greeks and knowing what to do, and I'm only in 195 BC, with a steady +20 000 to +40 000 each turn).

To reach this position, I simply build all the "money" buildings (traders, road, ports, etc.) with the exception of farms (never build farms, never), sign a lot of trade agreement, and then see the denarii cashing in. When I conquer a new city, I start to build the militia unit for the faction I'm playing (town watch for Romans, Hoplite Militia for Greeks, etc.). It makes a good and cheap police, and it can even work for repelling small-scale invasions.
Never had to bother about money at any time. If you upgrade your economy, and keep cheap garrisons, conserving your expensive and specialized troops for battles only, you won't have any problems.