When you have the tools but don't know how to make money.

I have some spare cash and a Google Ads account, but I’m not sure how to monetize them. When I try affiliate marketing, merchants often object to me running Google Ads. Does anyone have any ideas? Let’s discuss this below.

You can try Facebook ads instead. Regarding the Google ads, I think what the merchants don't allow is targeting the brand's keywords. But you can target competitor's keywords and this works very well.

I'd get the affiliate manager to confirm the PPC rules before testing competitor keywords. Are they restricting all paid search, or just brand bidding and direct linking?

Obvious one is affiliate marketing. You do need to choose programmes that actually allow paid search though A lot of merchants either prohibit it or have restrictions around bidding on brand terms. Might be a good place to start there and actually get somewhere than spend time skirting around the rules. Unless you already know how to do that reliable, that is.
If all else, you could use the ad budget to promote your own offer/lead funnel instead of relying entirely on affiliate commissions.

Google ads still works well with paypercall lead generation offer. Signup for paypercall affiliate networks, there are mainly 4-5 well known ones. They all not only allow but encourage google ads.
Work with those who wants you and align with your marketing strategy.