First of all, most alkaline batteries are not re-chargable and will leak a corrosive fluid if you attempt to recharge them.
While charging NIMH, even at lower than expected current, the 9V battery voltage will rise fast at first. But this doesn't mean the battery is anywhere close to being charged. As charging progresses, voltage rise becomes much slower.
A fully charged 9V NIMH battery will charge to about 10.5V to 11V and even then without connecting it to a circuit for use, the battery voltage will drop down to about 9.5V within 48-hrs. The normal charging current for a 9V NIMH battery is usually 35 to 70mA, depending on the capacity of the battery, and you should be able to see the recommended charging current v. time written on the battery case, with charging times from 8 to 24 hours, but this depends on the charging current. Slow charging is better for battery life.
A battery is charged to about 140% to 150% of its mAH capacity, since you need to put much more energy into a NIMH battery than you can expect to be able to get out of it in use. Charging any battery is not 100% efficient.
Overcharging can damage the battery and trickle-charging is not recommended. You can construct a simple timer using a 555 chip to generate 10 to 100-sec pulses that clock a CMOS binary counter chip (CD4060 for instance) to make an accurate timer. You can also cutoff charging when the charging voltage reaches about about 11 to 11.5V at the battery. If you like the counter idea, use some n-th output of the counter chip to reset a CMOS D-FlipFlop that controls a MOSFET that switches on/off the charging current returning to the charger. This charger-timer circuit can be a good electronics learning project.