The tradition in my family when I was growing up, for example, is that all birthday cakes must be homemade and hand decorated by at least two members of the family, working together. Scratch cakes are preferred but mixes are acceptable. Fugly cakes are also OK. But a store-bought cake was emotionally devastating to the recipient because it reflected a lack of willingness to put time and effort in to create something special. Odd? Yep. But every family develops its own traditions that way, and there are emotions attached.
... And you just pinpointed why, at my daughter's birthday party, I actually felt guilty that I hadn't made her cake. (For the record: my sister, who loves baking and makes excellent cakes, made the cake in my kitchen while I made a lunch for 20 people for the party. Like. No actual real reason for guilt there. But family traditions are powerful strings for guilt-tugging).
Things that work for my family in terms of channeling the gift-giving:
1) Start by accepting that my mother expresses affection via material contribution. Telling her 'no gifts' is, to her, saying 'you can't express love for your granddaughter. It's hurtful.
2) Express what we actually need. For example: "Daughter is wearing X size now, so should be good for Y size for winter and Z for next spring/summer. If you want to get clothing, those are the seasonally-appropriate sizes to get." And then we wind up with good-quality clothing that holds up to more than 1 kid and actually fits her during the appropriate seasons.
3) Work in a family hobby. For us... well, we read. I'm clocking in 70 books so far this year, and that's on top of a job and a kid and a husband and a life. We started reading to our daughter when she was 3 weeks old; she now requests specific books and will sit and be read to for 45 minutes straight. You wanna know what to get our kid? Books. Bonus is that they're easy to store. For my in-laws, when my husband was a kid, it was cross-country skiing (so outdoor clothing, mittens, extra mittens, contributions to boots and skis, etc). Work in what you guys do with the kid.
4) If people MUST buy large items, suggest things that are useful and have a longer life. Bicycle. Wheelbarrow. Contributions to a swingset or play structure. Sports equipment. Good-quality school backpack for a kid starting school. Lessons (sports? music? whatever the kid is into) for older kids (bonus: you don't have to store those!)
5) Make family values clear upfront. For example: violence, toy guns, gender-essentialist bullcrap, TV shows that include significant amounts of passive-aggressive social nonsense or a lot of whining (Arthur and Caillou are no-go, for my own sanity)... Also make clear storage/play issues: "We literally have no yard space for a play structure. We cannot have one. If we get one, it will be donated from lack of space. Instead, could you consider X, Y, Z thing that is actually useful to our family interests?", etc. Or, as I told my mom last year, "Daughter has 2 dolls that she loves, but you can't love lots of things all the time. Instead of another doll, what about some doll clothing, or a bath for her doll, or a doll carriage?" And, voila, doll stroller and toy bath arrived, and get LOADS of play time.
And, then, acknowledge that you can't control what people actually do, and have a large donation basket. In our case: my kid loves 4 stuffed animals and is indifferent to her other ones; new ones go straight out (non-played-with dust catchers I have to deal with, ugh).
Oh, and we rotate out toys, so only some of them are out at any given time. Looks less like clutter, and a toy they haven't seen in a month is way more exciting than the one in the corner they see every day (which then goes into the closet for a month and becomes exciting again).
