Hello.
As described on the side, its pretty standard lead acid battery, which may be charged with constant voltage. Requirements described in the table. In your case it is "cyclic use", so the voltage must be within the 7.2-7.5 volts and charging current less than 1350 mA (1,35 A). Practically any wall-socket PSU with adjustable to 7.5v voltage and max current about 1A must be suitable (ROBITON DN1000, SN1000S or like), if there is no additional charging circuitry inside toy, of course.
Before charging your MUST check the polarity of the PSU connector and charging socket on the toy, wrong polarity may cause damage of battery or/and PSU! Typically center pin is positive, but sometimes may be negative too. Try to find pinout on the labels or in the documentation. I think that wires from the socket (on your first photo) goes directly to the battery terminals, so in this case positive terminal of the battery must be connected to the positive pin of PSU connector.
Also, at least first time, regulary check the temperature of battery during the charging, its MUST not exseed 50°C. If it is about 40 degrees or more, disconnect the psu and let the battery cool down (actually, if battery in good condition and voltage and current set right they not heating so much).
Also, as say Mr.B, you can find suitable charger for 6v automotive batterys, but its like overkill for this case.