The basic idea is you find a rare unused token (like say f$#sdafad) and then finetune your image generation model with a specific set of images (say 20 images of your red cap at various angles) while telling it that f$#sdafad is the same thing as your red cap.
Then you can start prompting "f$#sdafad resting on the head of a monkey" and your cap will appear on a monkey's head.
The problem with this technique is the finetuning part. Finetuning can take minutes to hours depending on how many gpus you have and needs to be done individually for every new "token" you want to map to a specific individual or object you want to add to your pre-trained model.
Another strategy is to use some kind of autocropping strategy + generative infill. You can take a semantic segmentation model like Meta's "Segment Anything", then use it to segment out the item of interest manually (perhaps a UI could be built to make this a one-step process). Then take the mask and do a generative infill using some sort of image generation model like stable diffusion.
https://www.amazon.com/dp/B0C4YP8MKY
The third photo is my favorite.
Or... just Photoshop a person wearing the hat.
Or... just take a picture of someone wearing the hat.
Do you have an image of the cap in the right orientation, as it would also appear as it is sitting on someone's head?
If not, any algorithm is necessarily going to have to invent what the cap looks like from another angle, making up details on any previously-hidden side and guessing at the depth of different parts of the still image in order to rotate it into the right orientation
If yes, crop it out and paste it onto the target head
If you have to do this for only a few things, you can do it for a pittance through a service like Fiverr.
If you have higher or recurring volume, you can employ an offshore company to do this for a very modest monthly retainer.
Just let the provider on the other end figure out the tool that makes it cost effective for them -- AI or otherwise.
Can you link to an example image which you would upload and then describe based on that example what the generated image should look like?
Once you get that post right, using something like Krita with AI Diffusion should give you a nice fast process flow.