That's only about a watt and a half. What power supply voltage will
you run from? It should be easy to do with a single supply, capacitor
coupled output; a 4.7uF polypropylene cap would have around a third of
an ohm reactance at 100kHz, and very low loss. The 44H11/45H11 pair
should do well at this current and power level, and have ample voltage
ratings.
You might even find that an integrated "audio" power amplifier would
do fine, at a cost savings if you consider the sheer number of parts
needed in a discrete design and the cost of putting them on a board.
Also, over that small frequency range and low power, you could easily
transformer-couple the output, and use a pair of NPNs push-pull. It's
likely that one of the small MiniCircuits "RF" transformers would work
fine; at 4 ohms instead of 50, you'd get response to lower frequency,
and you'll find that even at 50 ohms they have quite a few models that
cover to below 100kHz. You could easily run from a single 3.3V or 5V
supply, or pick a higher impedance ratio to run nicely from 12V or
other voltage. For example, with a 12V supply, you can deliver 7Vp-p
with a 36:1 impedance ratio (3:1 turns ratio from _each_half_ of the
primary to the secondary). Lest you think that those small
transformers couldn't handle the power, I can say I just tested one
(TT1-6) at about half a watt, which is all my RF signal generator will
do easily, and it behaved well at 100kHz. I can't guarantee that that
particular one would handle 1.5 watts, but I'd expect some in their
lineup would.
Cheers,
Tom