You can maybe use defined units that are perhaps uncommon enough or variable enough to suggest value, so that trade can be based on valuing against that thing, without needing it present to act as currency. So, knowing ten bolts of fabric versus three sacks of flour against that working but past breeding age horse, might make it easier to value this loaf of bread versus that carrying bag against each other. It isn't a static measurement, either, since the value of a horse isn't set - the standard might be based on a number of factors, including age, health, and breed, so even horses would require individual valuation and haggling (and so not be "standard currency"). Or you might pick something like spices, whose entire value is in being used (and which grow staler over time) - and so won't be hoarded for currency, especially since value differs between spices, and even between batches of the same spice (based on freshness, fragrance, and potency).
Alternatively, you can value different things as "units" or "standards" used to measure goods against each other, and the lack of a common standard will prevent it from being currency - say foodstuffs are generally valued in terms their relative value to bread, while cloth items are generally valued in relation to maybe blankets - so bargaining eggs versus an apple would have both working out value in terms of bread, while eggs versus a skirt would be looking at matching those frames of reference (how many loaves per blanket, then backtracking from there). Since, these items will not be standard. Each loaf or blanket will still be of variable worth depending on its construction, provenance, and desirability - (I'd pay that for X's loaf, not Y's, and Z's blankets are always worth more...) so still not a standard currency since not any loaf will do.
Or, you could use time as a standard measurement - since obviously, a few hours of the town''s best seamstress is going to be worth more than a casual stitcher's, and no match at all for a few hours pulling weeds - but in general the effort put into something (or its scarcity, hours put into finding it) will let things be valued against each other in a very general sense, with plenty of wiggle-room for individual valuation of that effort left to prevent it from becoming a standard currency.
You will probably want a bit of extra wiggle room, in terms of allowing favors or debts, or delayed payment, to routinely make up part or whole of the bargains being made. That gives a great deal more flexibility for trading and making the community work as a whole, when individual wants and needs don't match up at the exact right place and time. You should also be aware that most bargains will be mixed trades (a bit of this and a bit of that, and also a favor for a consideration, will be much more common than one thing for one thing).
You might want to look at gift economies, which are community oriented and work by expecting people to be generous to those in their communities, with the expectation that those they help will be generous right back (and work by favors and debts more than straight out bargains).
You might also consider how even a "standard" unit of value or currency finds value in a trading style that deals in haggling, like most barter economies would, I assume. Even if a thing has general value (ie, everyone wants it), it isn't the same thing as being a standard unit of exchange since everyone, everyone, is still going to haggle over the price of it - and so exchanges between two things are likely to be individualized and variable, even if they are both measured against a standard valuable thing, they will be measured as standard examples of that thing (and both sides arguing for their particular virtues and the other's flaws, so it isn't a simple case of mathematics).