Hi John,
Are you aware that a "trickle charger" will take many, many hours to charge a fully discharged battery? How will you know when the battery is fully charged?
You probably need a "regular overnight charge current" circuit that automatically switches to a lower "trickle charge current" by a timer after about 14 hours. Then the battery can remain in the charger indefinately.
Let's start at the beginning.
1) What is the voltage and ma/hr rating of your battery? We can't think about a charger unless you tell us that most important information.
2) Measure the output voltage of your power supply without a load and tell us what it is.
3) What is the output current rating of your power supply? Connect a load so that the power supply is operating with its rated output current, measure its output voltage across that load and tell us what it is.
When we know the above information then we can calculate the overnight charging current, the trickle charging current, determine whether the power supply has enough output voltage and current capability and calculate suitable current-limiting resistors. Can you design a timer?
If you want to use an "idiot" diode to prevent charging a battery that is plugged-in backwards, you might as well use a full-wave bridge (4 diodes) so that the battery is fine either way.
BTW, you can charge from a 1000V or more supply, if you avoid the shock hazzard and limit the charging current to the same value as from a much lower voltage supply.