Can I run a little 7 VDC (1.2 watts) pump with a 9 VDC/0.5 Amp power supply? (The pump is for a drip to attract birds.)
You mustn't run a 7V rated device from a 9V power supply. It will probably work, but it will have a much reduced life time.
Cheapest solution that is somewhat reliable is to connect 3 diodes (1N4001 - 1N4007 will do fine) in series with the pump. These will always drop about 2V, in contrast to a resistor that drops voltage depending actual current.
With a resistor, when the pump runs dry, current will probably drop and voltage on the pump will increase and the pump may get damaged.
Best solution from efficiency point of view is to find a power supply that outputs 7V regulated or add a step down converter. Something like this:
which usually sells for couple dollars/Euro.
Unless stated otherwise on the pump manual/datasheet, you will need to decrease the voltage from your power supply to fit in your pump requeriments, if not you may damage your pump. I suggest a resistor based voltage divider if you want to stay cheap (keep an eye on the resistor watts, use at least 2w resistors).
You can find more info and a handy calculator about the voltage divider here.