You know, I think your question has been sitting here for a while because you are in a very niche market. I apologize for not having a prompt response.
You are right the equipment for this is expensive. Do your homework and post ads through craiglist. Ask on Quora about where to find or who has a piece of equipment that you can get for cheap or free. You will be surprised in the engagement.
Try also, reddit.

The magic in starting a business w/no cash is just pure networking but that takes a lot of effort and more time. But not more time than working and saving up to then pay up... So what's best? Well I think in most cases spending the time meeting people and making friends and spreading the word about your future business is better than saving up and just paying up.
As far as the trike (assuming you are using a trike) you can get one built out of pieces with about $150 here in the U.S. not sure about over there.

Get a small business loan or sell something for quicker funding. Sorry I couldn't be of any more help if at all. Best of luck :)

Keep me posted of when you "move your coffee" my twitter is @officialunthink

Hi.
I am a business coach and mentor with experience in many businesses. I make a point of studying different businesses, always looking for an opportunity and wishing to understand the viability af any model.
You may find that funding is difficult to find in the form of grants etc because you are basically going to be a sole trader. As you grow your business you will find that there are grants for employers that take on apprentices, which you may well be eligible to do. Currently there is a grant towards training of £1500 and this is to help cover your costs for training that person.
As regards the business, there is a good margin to be made here and one big tip is to research your machine thoroughly as servicing can be expensive and is essential. Also breakdown and waiting ages for spare parts will cost you a lot of money in actual bills and lost business.
Critical is quality of coffee and image, just look at Costa. Love it or hate it, their model works.
I think that the potential for this business is great if you get a good pitch with a high foot fall through out the day. At peak times you will have to be fast to get through the numbers.
It will be worth doing a study of similar businesses and note how many drinks they sell each, say 10 mins, and note the business through the day.
After the study, do some sums and try to calculate the numbers. It is also worth asking the vendors direct questions as you won't affect their business unless you are next door.
With the numbers you should look at lease deals for the machines, including the ones with repair/replacement on breakdown options. You don't want any down time!
I hope this helps.
Good luck with your venture.
Regards. Rick