There's not a good template you can refer to, as there is not one single right way to do this well.
Putting aside jurisdictional variations on how the rules for partnerships and corporations (or limited companies, depending on where you are), there is a simple and effective way to do what you want to do.
Sit down with this designer, and go over these important details:
1. what is your business currently worth?
While this can be a 'big' and complex conversation, keep it simple. Review all major assets the business owns, and look at the past year or two of revenue and profit for a benchmark of what to expect for revenue in the coming year(s). If there are special circumstances that may change next year's revenue from yester-year's - i.e., a lucrative new contract, a potential new distributor, etc.), then discuss how that changes the projections for revenues going forward. Go through this same analysis for profit (which requires reviewing your costs).
2. agree together what your business is worth today, and what it will be worth in 1 year, 2 years, and 5 years. Write this down, including the specific reasons why you (two) think so, from 1, above.
3. what is the designer's contribution / work going to be worth?
agree on an hourly rate along with set number of hours per month he/she will be putting into the business, OR agree on specific deliverables (focus on results with metrics rather than broad descriptions of what you hope will result from his/her efforts) - and then put a dollar value on those delivering them. IMPORTANT: write down what the cost to the business (or to you) is IF each deliverable is NOT delivered. This will be deducted if not fulfilled - and not more, nor less.
4. now you have the approximate value of the business, and how that may change in the near to mid term future. You also have the value of the designer's work or contribution, as it is proposed. Now, since you won't (can't) be paying him/her cash, agree on what percentage ownership of your business is a fair replacement of the cash he/she should have been paid. Keep in mind that the right number is the cash equivalent plus some alpha - some amount to compensate the designer for getting paid later (hopefully) AND for taking the risk inherent in any business (of failure, and therefore not being paid at all). Write this down.
5. Write everything down related to 1-4 above on a single document. Now add some boilerplate legalese - here's how:
(a) if you are not incorporated (or registered as a limited company), then look up some partnership agreements FROM YOUR JURISDICTION (i.e., your country, or State if you're in the U.S., or Province if you're in Canada),
(b) if you are incorporated, or the equivalent, look up share/stock option agreements and/or share/stock option plan documents - again, FROM YOUR JURISDICTION.
6. Add the appropriate boilerplate legalese from the documents you find per 5, above. For example, you will want a clause that describes what jurisdiction's law applies to your agreement, a clause that lists what venue you (two) are restricted to if bringing a lawsuit because of a disagreement, a clause about your document being the full and final expression of your agreement, a clause about the agreement being void if certain acts of God occur, a clause about each of you paying your own taxes, a clause about whether and how alternative dispute resolution will work, etc., etc.
7. print two copies of the document you two have now come up with, and both of you can sign both copies. Each of you take one, and voila - you now have the ideal structure for a contract that allows you to bring on a co-founder, without having to pay them cash right away.
Best of luck!