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As there is no more value attached to the cards I don't see how that would work. So I think youre stuck with either trading them 2:1 somewhere or try trading them with a human xD

if you are trying to trade them for marketable ones ... best you can hope is something like 2-3 for 1 ...

Fastest way: turn them into gem. It's the only value they still have.
Otherwise, you are probably looking for Thrash Dump, but you have to pick them one by one and trade.

I really recommend turning them into gems tho...

You can sell them on OPskins and then buy tradable cards you want, it might take some time but I did this a couple nights ago.

There are also some traders that collect unmarketable cards, best bet is to check the community hub for said game and look at the recent threads. Found a couple traders this way, take a look.

steamlvlup.com?

There is a guy on steam who will trade or give you gems for your non-marketable cards. http://steamcommunity.com/groups/tradingcards/discussions/2/135508292192047771/
You can also look at the trade forum for each game to see what other users are looking for. Might be able to craft the badge or just trade those cards away. There is also another Steam group who specialise in trading non-marketable items http://steamcommunity.com/groups/deaditems This one does not have a lot of members though.

I have 32 Not Marketable cards and I am looking to trade those from a few games for those from other games so I can still create badges for a few of those games.

For instance; I have only one card for Lemurzin so I'm looking to trade that for one of Frozen Drift Race or any other game where I need three or fewer cards to create a badge.

I have tons of cards, I am willing to trade all not-marketable ones as well. I'd also love to know a bot that does it since finding a human might be difficult.

https://steamcommunity.com/id/VanillaBot is a bot for trading non-marketable cards 1:1

well this necroposting has proven to be useful, I wasn't aware that the TrashDump came back to life!
I used it sometimes months ago but it stopped working for some weird reason..
on the other side, I use CouponDumpster basically every time I craft a new badge in order to gift every single coupon that can be useful to other players =P
anyways I found something happened in the gem crafting system some months ago - basically now we can craft card packs even for removed games while in the past it was impossible, I tried to complete some arcane raise/preraise etc. badges but since the games and the cards were removed from the market it's been a nightmare xD
it's been some months that I noticed I can craft packs for those games too with my gems and that's great, of course though I can only trade the duplicates, make gems and such because being removed games, you can't sell them anymore on the community market..