Here's how I would handle this with my sibling if i were in your shoes. I'm making the assumption that your ideal split is 50/50 but you're trying to work around your individual financial constrains to own the property jointly.
I'd start out clearly agreeing that we each own an option to own the property 50/50. What this means is that while we start out with uneven contributions, the person with the lower contribution has the right to catch up to even out your contributions.
For example, you buy a $200k property putting 20% down ($40k). Your sibling contributes $35k and you contribute $5k giving you guys a 12.5%(you)/87.5%(sibling) split. Over the next year, lets assume you pay all the expenses which amount to $10k. Your sibling still has $35k contributed while you now have $15k, giving you guys a 30%(you)/70%(sibling) split. This method would give you guys a continuous framework to measure percentage ownership of what was invested. Note: You really need to clarify what expenses are eligible to be added to the expenses. You don't want to fight over one person adding random gas mileage to their property expenses.
You guys would need to decide how to split any gains/losses in the value of the property. One way would be to use the same split from above. Another would be to agree upfront that its 50/50. Choosing either is totally dependent on your relationship and what approach you guys think works best for you. (the 50/50 approach to gains/losses becomes more relevant if you consider what happens at the outset when the split is really lopsided...lets assume a 95%/5% split for instance...if someone turns up to buy the property at a $1 million markup, do you split that 95/5 or 50/50?)
Things would get interesting if one person decides to leave and the other person does not have cash for a payout. A home equity loan might be an option depending on how much equity has been built up, but its no guarantee. You would have to agree ahead of time if such a situation means the property would have to be sold.
Getting into business with family is one of the worst but also potentially most fulfilling decisions people make. Tread carefully with open eyes to any potential landmines waiting to damage your relationship. Best of luck!