I don't know of any lower price gens that come duel fuel, myself, though do know there is a great propane/natural gas conversion kit for the Honda gens. I have one. It's from well-regarded Hutch Mountain. Because my van is diesel and I already carry propane for cooking, fire ring, and water heater, I prefer not to carry a third fuel just for occasional use of my gen.
Not what you want to hear, probably, though having run roads all over North America for many decades for both pleasure and business, and running across expediters, adventurers, and RVers who use small gens, I can honestly say that though many of the lower priced options may cost less, they often do not last as long, are often not as quiet, and are often not as efficient. I know several guys who got Ryobi or WEN or Powersmart, etc because they were lower-priced, who ended up getting a Honda after not being happy with their previous purchase.
Your mileage may vary, of course, though that's been my honest experience.
I picked up an AI Power dual fuel unit from Home Depot's website for around $350. I've only run it on a test run, on LPG, and it worked great! It looks to be more expensive these days but ou might be able to find something on sale.
I have the Champion 2500 dual fuel. @$500. Quiet as any gent 2-3 times that price can be scaled up by connecting two of them to back up a house. I love mine and will get a second one when opportunity strikes.