No you can't have infinite anything, there is finite space and similar restrictions that make infinite anything impossible. As a random example taking the idea to the absurd eventually you would collect enough coins that their combined gravitational pull is so large that you create a black whole, at which point anything you add to that point in space is unlikely to qualify as a 'coin.'
But I doubt that is what your really asking. So lets ask instead could you have an effectively infinite amount of money with this system?
First it depends on your time travel mechanism. For instance if an item in the past disappears when you bring it's future self back then no. Likewise if your time travel is the type where you can't actually change the past then probably not.
However lets say you are using something more like the idea of parallell worlds, where instead of jumping to your past you are creating a new dimension identical to your past save for your presence in it. In this case you could bring things back in time with you, and continue to collect more.
The process here would be simple. at time X you leave a large quantity of money (or other thing you wish to duplicate). At time X+3 you travel back to X+2 with all your cash and pick it up again in that time period, doubling what you have. Then travel back to X+1 and X and pick up the money there. You now have 4 times your starting amount. Leave that at time X, wait (or travel forward in time) until X+3 and repeat the process for exponential gains.
You may run into duplicates of yourself from previous time travel runs if you do this all in one place, so you may want to move your money making scheme to a new location each repeat of this loop to avoid run-ins with past(?) selves and arguments over who gets to keep the loot.
However, money would not be a good idea for this. Money is very tightly regulated in the modern era, the government will notice if you start spending allot of this money and will end up assuming your a counterfeiter and shutting you down. The further in the past you go the less regulated money is, but the less you can buy with your money that's likely to be tempting to a modern time traveler. You also risk inflation and hurting the countries economy if you take enough money back in time.
Instead your better off bringing precious items that can be sold back with you. For example you could start with precious metals like gold and silver which can easily be exchanged for cash at a later point. Eventually you would see deflationary effects, you sold so much gold in the time period that gold is no longer worth as much money since there is an excess of it available. However, if you did this process with a few different precious metals you likely will be able to exchange them for a sufficiently large enough amount of money to provide you with everything you would want to buy without deflation of the metals being too significant. If you devalue the metals too much use some of it to buy something with more inherent value, like say coal or oil, and start to duplicate that instead to sell. Though you still might draw some suspicion if you suddenly have a massive amount of precious metals or fossil fuel to sell and no obvious source for this wealth.
Alternatively, and possible easier, consider going far back in time, picking up a few coins and hiding them somewhere no one is ever likely to get to them, then travel to the future and dig them up. These coins will now have a very high resell value as collector items. It's easier to explain away finding a large cache of rare coins through dumb luck to avoid people asking questions and may be easier to sell them. To avoid devaluing the coins by selling too many at once hide coins from different time periods and geographical locations so you have many types of coins to sell, or hide other non-coin collector items that different types of collectors may be willing to pay for.
Note you can not bring the coins back to the future directly, if you did that they would look brand new and thus be suspected to be forgeries. You need to let them age the old fashion way while ensuring that no one finds them until you are ready to dig them up.
Still too much work? Come out publicly as a time traveler, duplicate your time machine using the same process described above, and hire someone to use the duplicate machine to help produce value for you. Or just sell the time machine. Create a (quasi...) post scarcity world for everyone.